yes the bis clutch plate doies fit the aircooled clutch, mine lasted a lot longer after the "mod", and i've also rebuilt a 126 gearbox, when the 1st/reverse went on my deville i took the box out stripped it into its component parts, i then took the box from my spare jet black 126 and stripped that down also, i then sorted all the bits from the 2 boxes and built a box from the best. The pictures in the hains manual for the aircooled 126, will be good enough guide it you need a bit of help putting it back together, you should be able to complete the whole job in an afternoon. I also, at the same time, removed the reverse light swith and wiring and put it in my deville allong with the ltd edition rear lights.
Not sure how you intend to get the box out, but when i did mine i took the engine out to give me working space, removed the gear box leaving the bell housing and final drive in place. I had no pit or lifting gear, not even ramps, just an old scateboard to move the engine on.