Rover got a fair way down the route of fitting an overdrive to the 2000 and it isn't clear why they didn't put it into production.
In practical terms today, the easisest fix is definitely that of fitting the V8 diff. The lower gear ratios seem to be low enough for this not to be a significant problem, at least with 2000SC, 2200SC and 2200TC, but you'd probably have to fit 2200TC carbs to a 2000TC in order to make the engine sufficiently flexible at low revs. Demetris is the originator of this set up and has some threads on it.
In terms of where to mount a double flange overdrive unit, I'm a little nervous of having two very short propshafts. That can give problems with balancing. In view of the relative frgility of the Rover box, I think I might want to mount the overdrive in unit with the diff, on the front of the extension, or even replacing some of the extension. The diff extension is much easier to modify than the back of the gearbox as all it contains is a single shaft that should be easy enough to machine a replacement for. If necessary you could even mount the overdrive back to front with the gearbox end facing the diff if you wanted to use the gearbox adaptor from another vehicle. The O/D is epicyclic, so it shouldn't mind which way it drives. That way you could get it to sit under the back seats where it might be easier to create space. but you'd really have to stand thoughtfully under the car with one for an hour or so, eying up where the space is.
Chris