Actually, the pilot bearing inside diameter is 0.669" (17mm) and the shaft outside diameter is 0.668". Most of the repair manuals say that the minimum diameter to use is 0.666" or it should be replaced. I have done a number of transmission rebuilds for members of our "A" club. I take the worn shafts to a local machine shop (owned by my brother) and they turn them down about 0.030 on the diameter and then build them up with weld and then put them in a lathe between centers and turn them to a diameter of 0.668". When I install the transmission into the flywheel pilot bearing I use LocTite Thread Lock on the shaft so it will not spin in the bearing. I refrain from turning the transmission for 24 hours to insure that the LocTite has set up.you are at the limit of wear. The bearing I.D. is .625, slip fit to the pilot (.001) with a tolerance of .002. Too loose will contribute to slipping out of high gear when coasting downhill. If your gears fit the main shaft snugly, then I bet it will work OK for a while, then start slipping out of gear some time further down the road. If your gears are loose on the main shaft, it might start slipping out immediately. I would replace it since I do not like pulling the transmission a second time if it were to slip out of gear and I want my machines to last reliably for some time. Some guys would take the risk and go with it anyway. I suppose it depends on how much driving you expect to do. Its your call.
When I install the transmission into the flywheel pilot bearing I use LocTite Thread Lock on the shaft so it will not spin in the bearing. I refrain from turning the transmission for 24 hours to insure that the LocTite has set up.
Refering to the quote of Pat from Santa Cruz, I understand that there is a bearing available with a 0.625" inside diameter. I would not use that because it would make it a nonstandard shaft in the event that the bearing would need to be replaced in the future. This is obviously a personal preference. I believe there was a thread recently referring to that special 0.625" id bearing, but I looked thru the first 20 pages of postings and could not find it. Hope this information is of value. Don/WI