As Les Smith's first reply suggested, your problem is probably in
the  upper  or  lower  brake pressure.  The slippage problem does
easily occur toward  the  end  of  band  organ rolls, unless  the
tensions of  the  two  brakes  are  adjusted just right--and this
takes  some   fine  tuning  to  accomplish.   The  difference  in
circumference between that of  the take-up spool and that  of the
roll  on  the  top spool is  not large at  the beginning of play,
because the bare take-up spool is large and  the  band organ roll
itself is equally large--much larger than  any  piano roll.   But
the difference gets very great toward the  end  of  the roll,  so
that you have a very large take-up spool trying to pull paper off
a small-circumference top spool by causing it  to turn, the force
required for which is much greater than it  was when the top roll
was large.  The result is  that  the drive train, which keeps the
bottom spool turning no  matter what, causes  the  paper  on  the
bottom spool to tighten up on itself, if there is any room for it
to  tighten,  as  soon  as   the  force  required  to  cause  the
self-tightening is less than the force required to pull the paper
off  the small-diameter top spool, which, remember, is restrained
to some degree by its brake.

On  a band organ, the other factors such as paper surface texture
and degree of drag on the paper caused by tracker bar suction are
(from  my observation) minimal factors in  the equation, although
they may be significant factors in a piano roll situation.

Keep adjusting and you should lick the problem on all  or many of
your large rolls.