My father and I changed my BJ8's differential from the stock 3.9:1 ratio to a 3.45; this mod was the most 'extreme' one I've made to either of my Healeys, as far as changing the whole 'Healey Experience.' Since much of our driving in the USA has to be made on 'freeways,' unfortunately, I feel this change was almost required, as spending hours on end at 75MPH+ with the shorter rear-end is fatiguing to the point of torture. The taller 3.45 is an 13% reduction in RPMs at every speed, and the 300+ RPM reduction is significant. Yes, you'll sacrifice a little 'off-the-line' acceleration, but with a stout engine it's not a big deal and Healeys are not great dragsters to begin with (a modern Corolla with an automatic will beat you off the line).
As for installation, we used dial calipers and I think we did a decent job, as my father was an excellent mechanic but, yes, I have a bit of a whine which is usually only noticeable with the hood up. I've heard from others who've had 'pros' do the job and still experienced the whine, but some who had professional installation say theirs are quiet (it's what you could call a 'crap shoot'). My dad was a factory rep for Ford when the Mustang debuted, and he said a lot of those cars were brought to dealers with 'noisy rear-ends,' so it's a not uncommon issue. About the time I made the change I experienced some judder from the drive train on launch, but later when I rebuilt the gearbox I found a couple broken damper springs on the clutch disk, since that was remedied no more judder (but perhaps a slight bit more slipping is required to get a smooth launch).
There is a requirement for various spacers to set offset and backlash--we were able to reuse mine--which may be difficult to source, though the Healey (MOWOG?) differential is said to be very similar to contemporary American units. Backlash is set with a spacer instead of a crush washer, if less spacing is required the spacer can be milled down, but if more is required a larger spacer would be required. Of course, you can replace the bearings while you're at it, but mine were still serviceable at 100K+ miles. I like and use synthetic oils in both my Healeys' gearboxes and rear-ends. There is a specific break-in procedure for differentials; usually, it's up to 500 miles of increasingly longer drives, with a mandatory cool-down period in between. Your gearset should have included instructions; they may specify not to use synthetic oils for break-in, and you'll want to change the oil after break-in).
Overall, a very good mod, IMO, esp. if you can't take backroads everywhere you go. Some even recommend the 28% O/D as found in the 100s used with the taller rear-end; that would make an excellent grand tourer.