I think the "short of replacing the BB" bit is probably the sticking point!
Seriously, though. I presume you mean that the crank is binding on the cup
, not the shell
(which is part of the frame)? If that's the case, is there any chance that a different cup might help? Different cups are different thicknesses, and if your cup seems to protrude quite a bit (the old Stronglight cups did, for example) then a replacement might help. Unfortunately, it's likely to involve quite a bit of trial and error, though.