If the stack is cold and the numbered pneumatics can be easily
knocked off, the passages of the stack can be resealed with shellac
and the pneumatics hide glued back on, cracks and grooves matching.

If the works have already been compromised with wonder materials,
try to scrape and brush down to the wood, shellac seal inside and
level with hide glue on the mating faces.  Trim excess away with
a knife when it is firm but not crunchy, then apply the flattened
pneumatics.  I have seen talc filler used in hide glue for this,
but I haven't needed enough fill to fiddle with it.

There are architectural fillers intended for "permanent" repairs for
the most decayed posts or window frames which look lovely when the
repair is complete, but in my architectural restoration experience of
only 48 years, have seen them look like a ten-year-old toupee by the
continuing rot at the bonds and fall off in massive hunks.  It is no
sin to replace a piece using the original material and techniques
unless the instrument has its own board of conservators trying to keep
it totally original.

For your flaky stack, I would scrape and brush the offending material
away, assess the condition, and finish it a manner which will elicit
praise from the next technician who has to do next.

I am now reversing some ill-advised mods to an 1785 music maker which
was the iPod of its day, (superceded by those upstart music boxes), and
see that the perpetrator has wisely omitted writing his name on the
work, perhaps guessing how I would use it.

Karl Petersen
Washington, Illinois