I recently acquired a 1967 Miyata commuter with a Shimano 333 internal hub and twist grip shifter. The gears, however, do not shift (although they did at first--I must've messed up the hub when futzing with the gears, which tells me they were ready to go anyway). Knowing how difficult it can be to repair the 333, is it possible to replace it with a Sturmey Archer AW hub? Would I be able to use the existing grip shifter? My concern is that the dimensions won't jibe.

Ideally, I'd like to keep all the original components so I am going to try to repair the 333 anyway, but I want to know what my options are.

Thanks!