While you are close to it a quick look at the diff pin would be a good idea. Also while you have access turn
the first motion shaft slowly and listen for a clack clack as the first motion or third motion balls bump together 
due to the plastic spacers breaking up. Steve (CTR)

Glad you found it. Had the same issue with a friends car a bunch of years back.

Hot Damn Willie!!! You were right! The right side drive flange splines are almost completely smooth! I can’t thank you enough! Of course now I have to put the engine, which didn’t have to be removed, back in, etc. At least now I know what was wrong.

My car is a 1993 with 12” wheels. The link you provided refers to 10” wheels. Does the same apply to mine?

Did you check where the cv shaft connects to the drive hub, If one goes bad the car will not drive at all.

https://www.minimania.com/part/21A1270/Classic-Mini-Drive-Flange-Cooper-S-Disc-En24t

I have both driveshafts out of the car and the engine removed. In removing them, they seemed to be in normal position and all CVs seem intact, although the gaiter on the left hand outboard CV was badly damaged and the spline of that CV was seized into the hub bearing. I got it off, and will be replacing the bearing and that CV joint despite the fact that it seems intact. I don’t think I have found the source of my problem yet.

I refer you to my earlier comment about driveshafts and CVs.

It's perfectly possible to pop the CV off and you can't tell from the outside if the boot is loose on the shaft.

I just took the flywheel cover off and everything looks normal. There was a little dirt at the bottom of the housing, but nothing I’d call debris.

Well, the mystery with Brutus continues. I’ve got the engine out and have removed the differential, which I’ve thought after the driveshafts seemed okay was the source of the no-go status, only to find that it looks and feels absolutely intact! I suppose the clutch could be the culprit, but would it just suddenly fail completely?

Well done, take photos as you go, lots of labeled plastic bags of related parts, bolts back where they came from when you can. 

Well, the engine is all stripped, leaving only the transmission linkage and engine mounts to be removed to pull it. Lots of frustrating hidden bolts, etc., but none broken! 

Okay, Steve was right. The left axle is out and no obvious CV failure. On to pulling the engine. There’s a great deal of servicing, rehabbing,and replacing to be done throughout the front end and engine compartment anyway, so it’s all good. Tally Ho!

Yes, out the top is easier if you don't have to deal with injection. Do check the plastic ball spacer on main shaft bearings.
The DAM 5626 trannys suffer from both problems. Check first/second shift fork and second synchro it catches it up and
down shifting. I have a couple of complete gear sets but short on cases. Steve (CTR)

Mine is a carburetor model, fwiw. Hoping that once I’ve removed the various fitments that I can pull out from above. Also, obviously, that the damage is limited to the differential pinion gears. We’ll find out in the next while, won’t we? Wish me luck!

I have had to repair several of the late injected cars and pulling the power is a bear. I attach to the engine and lower it complete with the sub frame by lifting the body. Considering the bearing and spacer issues these suffer a complete tranny rebuild is in order. There are two issue they suffer. One is the diff pin failure and the other main shaft bearing failure. The ball spacers break up allowing the shaft to run off center. The last one I did I threw away everything to do with the tranny. The damage was so bad I even threw the bolts away. I'm getting short on rod change cases and have run out of remote ones. I used up my four synchro AA cases building magic wand units for Mokes. Steve (CTR)

I’ve been doing a lot of research watching the wonderful YouTube videos out there, which has increased my confidence and in excitement in proceeding with this project. I wish I’d done so long ago. From what I’ve learned, I think Steve is probably right that the differential is the most likely culprit. I’ll soon have the other axle out and expect to move on to pulling the engine.  

It's very possible to pop the end of the driveshaft out of the outer CV when doing a full lock turn on power if the circlip is duff or missing.

Suzy did it a few times on Tigger before I changed the CVs and circlips.

I guess it might come to that, Steve, but I’ll have to convince myself there’s no other alternative first.

You need to bring it up here and I'll fix it. It won't be easy or cheap it can be done. Steve (CTR)

Well, sadly I guess, the problem doesn’t seem to be with the right inner pot joint, as I’ve got it out and everything seems intact and in good condition. The boot needs replacing since I tore it a little at the axle end, so I’ll have to take the race off the axle to do that, and I’ll clean everything up and repack it. 

I guess my next step will be to pull the left axle and see if all is well over there.