There are a number of factors involved in this problem so I will
deal with them one at a time.

The organ has a keyless keyframe so this requires that the grooved
roller provides sufficient force to hold the book against the tracker
bar without allowing any leaks, and hence ciphers.  Excessive force
will cause premature wear to the tracker bar and also create an
excessive drag onto the book.  So the first thing to check is that
you haven't got excessive force on this roller.  The force should be
just enough to prevent ciphers, and no more.

The book is pulled through the keyframe by a pair of rubber rollers
which grip the book from above and below.  The bottom roller is mounted
in fixed bearing and the upper one is mounted in sliding bearings
within the top of the keyframe, and sprung downward by a leaf spring,
or equivalent, which is adjustable by means of two screws.  This spring
must be tight enough to pull the book through, and no more.  Excessive
force between the rubber rollers will create excessive drag to their
rotation.

Once you have regulated the keyframe you can turn to its drive
mechanism.  It may be that the belt will no longer slip, but let's
assume that it still does.  The torque transmitted by any belt drive
is proportional to the belt tension and the coefficient of friction,
assuming that other variables such as pulley diameters, are fixed.

Many belt drive keyframes that I have seen have a double pulley
arrangement where a single belt passes around the pair of pulleys at
each and, with a cross over along one side.  This immediately doubles
the torque transmitted.

Assuming your single pulley arrangement is original there must be
another problem.  The manufacturer clearly designed a system that
worked, and I don't believe for one moment that it would only work
if the owner applied some form of friction enhancer.  Any correctly
designed belt drive will never require any form of magic potion in
order to make it work, so we can discard that idea.

You need to check the pulley cross section.  If may be either
semi-circular or of inclined sides with a flat bottom.  In either of
these, if the belt diameter is too small it will sit at the bottom
of the pulley rather than sit closely fitting between the sides.
Sitting on the bottom it will be no better than a flat belt whereas
if it grips the sides its effective coefficient of friction will be
significantly higher.

This is the principle by which the V belt transmits significantly more
torque than the flat belt -- the shallower the angle of the V belt, the
greater the effective coefficient of friction, and therefore the greater
the torque transmitted at any particular belt tension.  Concluding
therefore, if the pulley is of circular section, the belt must be of at
least the same diameter and if the pulley has angled faces and a flat
bottom, the belt should sit half way up the sides and not touch the
bottom.

Check all of the above and your organ will work faultlessly.

Best regards,
Nicholas Simons, UK