Bike Forums - Schwinn Continental BB conversion issue-65 mm shell width

I am in the process of swapping the one-piece crank to a three-piece crank on an old Schwinn Continental. I purchased the Truvative American to Euro BB adapter and installed, but noticed the bolts to connect the halves of the adapter protrude past the opposite piece (fixed cup side). So this prompted me to measure the BB shell; it is about 65 mm wide, not 68 mm. I've done some searching and apparently some really old bikes have a sub-68 mm shell width. I don't want to bother looking for a smaller bottom bracket spindle, and I'd like to use the 68 mm one I have lying around.

I was thinking about putting a spacer so that the fixed cup doesn't screw all the way in to the adapter. This would mean about 3 mm of threads will not be engaged by the fixed cup as to accommodate the longer width 68 mm bottom bracket properly. Does this sound like a viable option? Any suggestions would be greatly appreciated.