The transmission failure is quite rare. I would just fit a new radiator and be done with it, that's what I did when I bought mine. I did fit an oil cooler to my last one, but changing the radiator is sooo much easier, took me just over an hour.
I did very briefly go back to an LS400 last year but it just felt aged by comparison. That wouldn't of course stop me if a really nice genuine one came knocking on my door!