If I was you I would install an aftermarket transmission fluid cooler and bypass the radiator

Confirmed: the automatic transmission cooler connections won't match mine (see picture below). Is that something I can fix with some sort of adapters or does it need an entirely different model?

Attached Images

       

It is quite an ordeal to get a matching part for this car in the UK, and I'm still just trying to figure out if I have a blown head gasket, so I'm not entirely sure I should invest in more parts before even getting there?

Good point. If you are just trying to get it to where you can drive it some (not far or for long) you could use a piece of metal pipe to loop the transmission cooler lines together. Just a thought if you are in a pinch

I'm mainly trying to start a pressure test (short use indeed), but overall it's better not doing the same job twice, so I'll probably just return that part and find another one, hoping for the best.

Just a random thought at the moment (because I'm fearing it's the cause of my blown radiator), how come replacing a head gasket on a 4Runner is that immensely labor expensive (compared to some other cars)?

The ‘96-‘09 Land Cruiser Prado (J90 & J120) and the Toyota Hilux 167 series pickup came with the 3.4L so you might be able to find parts over there for it.

Just curious, are (used/junkyard) engine swaps relatively easy in the UK or are they mired in regulations, in addition to lack of donors, etc.?

I like the idea of joining/capping the transmission cooler inlet/outlet while doing a head gasket test. I have used a simple and cheap kit in the past that tests for combustion gasses in the coolant caused by "Blown Head Gasket, Cracked Head or Block, Pulled Bolts or Studs, or Warped Sealing Surfaces" It put my mind at ease on my 2nd Gen that had a mysterious fluid loss before I sold it to a friend. Turned out to be a faulty heater bypass valve.

Like this: Amazon.com: Block Tester BT-500 Combustion Leak Test Kit - Made in USA: Automotive

Not sure how complex that would be here, just moved here a couple years ago with my Canadian truck after driving it all the way to Panama

Lack of donor would certainly be the first issue in mind. I know less than a handful of scrapyards on eBay with 3rd gen Hilux Surf (all RHD diesel) and never seen any 4Runner anywhere. 2nd gen is a bit easier as it was sold here (probably different specs/trims still).

Problem for the 3.4L in Europe is that, in the eventuality it existed, it just wouldn't sell because of the gas price. I remember when meeting other overlanders during our trip, most Americans would always tell me they liked the 4th gen better because of the V8, while ALL Europeans would drive 4 cylinders of whatever vehicle they had (often diesel). And A/T practically didn't "exist" until 2000 in Europe.

Update: radiator finally changed, and the pressure seems to have been a false alert with the water pump doing a bit of extra work on startup! Up and running again, thanks all