I recently purchased and rebuilt a Gem roller organ, and had to re-adjust
the cob carrier rack.  There are two adjustment screws (with stop nuts)
on either end of the carrier mechanism (under where the carrier arm
curves downward).  By loosening both screws and backing off the locking
nuts, the mechanism can be moved side to side to adjust the alignment.

My cobs were not tracking correctly either, and the song would be into
the first measure after it snapped back to the start.  By moving the
carrier incrementally, and tightening the screws and lock nuts, I was
able to re-align the mechanism.  It took a bunch of trial and error!

I too would be interested in identifying cobs.  Unfortunately mine have
the labels completely worn off.  How would I transcribe a cob to Midi ?
;-)   Hope this helps,

Scott Currier