As a restorer of original instruments, I too have run into my share of
white glue nightmares. The best solution I've found for dealing with
it is to use a heat gun. It allows the surface to heat up enough to
remove leather, cloth and wood from wood, without warping the wood or
causing any damage.  Granted it does take some time to work section by
section, but less work than re-making whole components from scratch.

Cheers,

Stephen Kent Goodman