Use of Mini gearbox - there is a built in weakness in these as made by BL - long time ago but I recall getting quite good at lifting the engine, removing the gearbox, changing a ballrace and putting it all back. The weakness is that for the saving of some pence they used a plastic cage in one of the races on the mainshaft which breaks up and if not dealt with immediately seriously knackers the rest of the box. I imagine that some progess has been made over the intervening 40 years and that someonee can tell you what to use - I just used a better quality race with a steel cage. Needs looking into.
This little engine shouldn't give the gearbox much to worry about except how to change on the move, probably best to remove the synchro rings.
Ideal would be one of the compact Fiat or Ford variable speed transmissions, but they have efficiency and reliability issues as well.
Issigonis muted some alternatives in Dec 65 Motor magazine, including the use of a torque convertor with a steam engine!
Know an ex NEL engineer who worked on one of the Issigonis steam powered hydrostatic drives, another absolute disaster.Imagine a Weir steam pump pushing oil around some motors, water rate must have been horrendous. All patended technology.
We have a Fiesta with the CVT automatic which is completely brilliant - so much so that we have kept the car for 10 years in preference to swapping for some other inferior type of auto. Ford withdrew the CVT Fiesta in 1998 although I see they now have a CVT version of the Focus. The common problem on the Fiesta CVT is wear on a valve whose piston moves in an alloy valve body - another penny pincher - the cure is a steel liner which we had done by an independant auto repairer at 42000 miles. Economy is 3-4mpg worse than a manual at a guess - averages 35mpg. I think it would be very hard to adapt such an auto to your steamer as I suspect that along with most modern automatics it is tied in to the engine management system to control its response to load and throttle. Certainly the first CVT Fiesta we had was inferior to our second on a winding road as it didn't seem to know what to do at light throttle. The second car is superb - just like an electric.
For complete simplicity how about a chain drive - like the vintage GN - two pairs of chains and sprockets with sliding dog engagement - give you neutral as well and very easily made in your shed! No doubt if you were really ingenious you could find a way of incorporating synchromesh or even clutch engagement of the low or high sprocket which would give an idiot proof smooth change.
Simple and idiot proof, way too much to ask for!
Chain is good, there is a number of motorbike sprocket arrangements available off the shelf at low cost.
Have considered using a Triumph (dreaded BL again) differential unit and mounting the engine longitudinal on top. Allows access to the cylinders without removing the engine but gives me new problems with mating the drive shafts.
Scrapped my original final drive because I had not allowed for the torsional stress on the nose of the engine case. The B&B engine must be held by the mounting pads on the side of the crank case, pity they had not made a mounting flange around the output shaft.
Another thought - if you put a chain sprocket directly on the crankshaft the bearing loads would be quite different to the design loads which presumably anticipate the crank driving a shaft in a direct line. You might need to mount the driving sprockets on a countershaft with bearings and a coupling to the engine.
Problem arises with the extension required for two sprockets and dog clutch. For the ratios required to drive the Mini diff. sprocket diameter is small, in the 2" - 3.5" range. Driven sprocket limited to 7.5" max. Triumph diff.(if it fits) would allow wider choice in sprockets but again a layshaft would be required.
Plan to spend Saturday mocking up yet another design, I work better with plywood than Turbocad.