As a MK 1 GT6 originally non-overdrive owner here are my thoughts for what they were worth - It depends on what you want,what you care about, and how big your wallet is!
For me it was - Cost / Reliability and Originality (to some respect). My original gearbox was quite tired and pretty sloppy,I was not happy about the cruising speed on longer runs, but I didn't want to fit something that just doesn't belong!
So, purchased a Mk 3 box with J Type o/d and all the ancillaries, This was re-built, and also fitted by Mike Papworth. I kept the same rear diff as mine is lovely and quiet. There was a tiny bit of tunnel removed (A few inches) to make the fit easier. mike got me a new prop shaft to fit, there's no point in my mind to getting them re-built as they are not expensive new, in fact its the same price to refurbish so why bother?
My engine is not the original either so another reason I was not worried about the Mk 3 box, plus I was advised that this was the best of the Triumph boxes
This was the least expensive option I could find for the quality so how big is your Wallet ?? Leave it to you
Aidan