Sorry it's a month late but I'll also chime in for some more perspective.
Vellfire or Alphard? I think this is really a personal preference. They share the same platform and engines etc. they are just marketed at different customer bases. Alphard is marketed as the premium family focused car with a more conservative appearance. Vellfire is the sportier version aimed at the younger crowd with a different front grille, headlights and clear rear lights. Interiors are pretty much identical, there are some colour combos that are exclusive to each but you mostly see black or beige interiors with various red, brown or grey wood accents.
Based on my Elgrand spec, which versions should I refine my searches to? Based on your Elgrand spec I think you would be looking for at least a "G" package or above. The trim levels, at least for the 2012 (the year I got so where most of my knowledge lies) went "X" "S" "G" "S C Package" "G L Package" You can also find the "Royal Lounge" but honestly unless you only use it to chauffeur around two rear passengers it's not worth looking at. The standard "G" package has higher grade upholstery, leather seats as an option with either 7 or 8 seats. Dual power sliding doors, power front seats and rear climate control. Sunroof, power tailgate and upgraded audio were all optional extras. A lot of the features you list for your Elgrand can be had on the higher spec Alphard/Vellfires but there were so many options for all the trim levels and sometimes the trim levels aren't listed in the adverts so you have to look through the pictures to try and spot the features you are after. In any case the front sunroof only pops up the rear moonroof opens completely. If you want rear facing middle row seats you will be limited to the pre 2008 10 series as they were removed for the 20 series onwards. Cruise control is pretty much standard across the board. You can get Radar cruise and Lane Keep Assist on some of the higher specs. I absolutely love the radar cruise on the motorway. Blinds/Curtains aren't fitted on the 20 series as standard, you can buy third party alternatives though. 360 cameras are also available but again will be a tough find and usually found on higher priced models.
What models/years/configs to avoid? Here's a link to the catalogue showing all the various options https://www.toyota.co.jp/jpn/company/history/75years/vehicle_lineage/catalog/60000926/html5.html#page=1
Is hybrid available on older Vellfires? The Hybrid was introduced to the Vellfire in 2011.
Are they all ulez compliant, regardless of being hybrid or not? You should check the number plates on the gov website, but everyone I checked is regardless of engine. Somewhat of a loophole in the system, probably the same reason that we only pay £345 tax when a UK car of similar age and spec engine would likely have been over £700.
Is the indicator stalk on the left? It's on the right in my Elgrand, they can be swapped if you are suitably skilled/confident (I am neither of these ) It is on the right, I think they can be swapped but I've never looked in to it as I actually prefer the stalk on the right.
Are the buttons and any on screen menus in English? Elgrand buttons have some in English and some in Japanese! The on screen menus can be changed on newer models with a magic box from some guys in Russia. Unfortunately, mine is too old for this. This is a tricky one, as there are lots of different model headunits out there. I know that my 2012 has an option for some English on screen (still a lot of Kanji regardless.) The model number on the front of mine is 56107. Older models don't have this option. Apparently the only way to get English is from a non JDM import but I have honestly never seen a non JDM for sale in the UK.
Do the radio's support Apple CarPlay? Nope, they are pretty antiquated but keep in mind these are now pushing 17+ years old. I actually read a write up recently about ICE in Japan and it seems very common for even modern JDM cars to have pretty basic features on the headunit. You can get a massive amount of different types of replacements though. Mostly Android units that have CarPlay and Android Auto. You can even get a Tesla style tablet to replace the centre dash. It can be a pain though if you intend to keep things working like the 360 cameras and video to the rear TV screen. I have stuck with the original unit as I like the G-Book feature that tracks your average fuel consumption. I just use Bluetooth to stream the radio from my phone. Another option is to get one of those portable CarPlay screens, most of which have wireless CarPlay, so you can stick it to the dash/windscreen like a sat nav and still keep the OEM features of the headunit. I'm going to be looking in to these in the next couple months myself.
Does the speedo also indicate mph? The Elgrand was kph and I had a new panel fitted. The odometer is digital and fixed at kph. The place I bought mine had it electronically changed to Miles. Rather than replace the panel they have put an MPH sticker over the KMH on the physical dials. The digital reading on the dash has had a tiny black sticker placed over the "K" so it just reads m 😂 Apparently even though you can change the ECU to show the numbers in miles you cannot change the display to show MPH/MPG, so the car shows you average mileage as X.XXkm/l at first I thought I was just getting really bad fuel economy until I realised the numbers were representing MILES per L not KM per L I seem to average 5.3m/l in my 3.5 V6 which is about 24mpg. Range is also displayed with a KM rather than M. The only thing that has stayed as true km/h is the cruise control reading which maxes out at 117km/h.
Are most of the commonly used parts readily available? I can't speak for the Hybrid, but as far as the Petrol goes it seems pretty easy to find most of the common parts you would need to change. IT shares a lot of parts in common with other Toyotas in the UK. Brake pads, filters, spark plugs, battery etc are no harder to find than any other UK car. It's the things like headlamps and body panels that will be a real killer if the worst was to happen. Frustratingly little things like the TV remote for the rear TV have a habit of going missing during import. Trying to source one over here is possible but you are limited to horribly expensive third party options on eBay. I ended up going through Buyee to purchase a second hand one direct from an auction site in Japan for around £40 including all shipping. Going direct to Toyota would have cost over £200 and that's if they even had any inventory left. Another annoying thing on the 20 series is that the lights that light up the A/C controls are LEDs soldered to the MoBo so if one goes you have to be handy with a soldering iron to replace it or again try and source from Japan. The tricky part is that the part name is Air Con Cntrl Assy and because of the word Air con being used it gets flagged as a restricted item so it get's tricky trying to import it even though it has absolutely no gasses involved.
Any recommended dealers that would be open to part exchange? I live in Surrey and happy to travel for the right car. I bought my Ellie from West Yorkshire. This is a tough one. I wouldn't recommend the place I bought mine from, but unfortunately it was the only place at the time that had the trim and spec I wanted and short of importing one personally I took the chance and travelled down south to purchase. I had really good experiences with Stuart Spencer Autos in Tipton. Really helpful there and were more than happy to let me and the wife to take a look around a lot of their stock. Only reason I didn't make a purchase with them was that they didn't have the spec I was looking for. They also take other imports as part ex too, a lot of the place I spoke to were happy to take imports as part ex. Not so keen on UK cars though for obvious reasons.
Has anyone used an importer and achieved a happy outcome? Can't help with this one. I was very close to going this route as you could easily save yourself a good few thousand pounds by doing it yourself. But I was more than happy to pay the premium to one that was already imported and sorted to drive away. I don't think I could take the anxiety of the whole process, especially once it's on the ship.
I'm easily distracted by shiny things and would welcome your thoughts if this, constitutes good value? It's a beautiful looking Vellfire. I would compare to your Ellie specs though, it has no sunroofs, no power tailgate, no side cameras, only one power door by the looks, is 2.4l. 14 years old and 72,000miles. £12.995 seems a tad high. I paid £2,000 more for my 2012 Alphard, granted it is the 7 seat version but it has the full black leather, high sided electric middle row seats, power tailgate, power slide doors, 360 camera, radar cruise, LKA, heated, powered front seats with drivers side memory, 18 speaker theatre system 3.5l and 10,000miles less on the clock. My advice, find a dealer that has a decent amount of stock and go take a look around some. I think we travelled about two hours the first time we went to look at Elgrands and Alphards. I was actually dead set on buying an Elgrand until I sat in both that and an Alphard. It wasn't until I'd sat in them and a few different trims that I started to nail down what spec I actually wanted. Once I did that it made looking online so much easier because I could tell straight away from the pictures if it had what I was looking for and could instantly toss it aside and move on to the next one. I would say something like this is more towards the spec you would be aiming for https://www.autotrader.co.uk/car-details/202407161826239?fromSavedAds=true&advertising-location=at_cars&sort=relevance&postcode=NP19 4SG I fear you will likely have to make some sacrifices though if the 8 seats are a must as they tend to be part of the lower end trims that omit a lot of the features you mentioned.
Is the criteria of newest model and lowest mileage the most appropriate? Or are high mileage examples likely to run and run? From the looks of it these cars are pretty bullet proof. The only common "failure" I have seen mentioned is the water pump leaking. What I will say though is that the 3.5l V6 has a timing chain rather than a belt. So this is expected to last the lifetime of the engine, of course it should be checked over at major service intervals. The 2GR-FE engine typically lasts between 250,000 - 300,000 miles. This is the same engine that is used in the Lexus RX, RAV4, even the Lotus Evora. I would 100% go for the 3.5l on the 2nd gen models. The first gen (02-08) 2.4l 2AZ-FE uses a chain. 3.0l 1MZ-FE uses a belt. Second gen (08-15) 2.4l 2AZ-FE and 3.5l 2GR-FE both use a chain. Third gen (15-Present) all use chains.
Do some models have twin electric sliding doors? Yes.
Do some models have a powered tailgate? Yes.
Hopefully I've been able to give some useful info there. I'm more than happy to answer any other questions you might have.