I do not intend to sound harsh, but as a retired player technician I can
tell by your question: "How hard is it to get parts for a Kimball Player",
that you will be better off trusting the restoration to a reputable player
technician.  If you are somewhat handy and mechanically inclined, you
might do the work yourself, but under the strict supervision of an
experienced player technician.

To answer your question, most of the parts you need are right in front of
you, within your piano!  They are in need of thorough restoration.  (Every
square inch, no patches, and nothing overlooked!)  If this is followed
exactly, a good restoration can last another fifty or more years.

Restoration is very exacting.  The temptation for the novice to use modern
glues, wrong types of materials, as well doing serious damage within the
player and piano itself, is taking a great risk, and it usually ends up
making matters worse.

With much experience in this field, I can say that I have run into fatal
and hopeless messes created by the novice rebuilder.  These nightmares
created by the home-style rebuilders can cost up to _five_ times more
to correct, than if the novice had the work done by a reputable player
technician the first time around.  Some end up hopeless and can never be
restored without excessive measures and expense.

An example of this: I found in a piano which the owner suspected leakage
around the flap valves in the pumping bellows, and glued them to the
surface!  (Because there was air escaping!)  Another inventive home-style
restorer recovered all the striking pneumatics with plastic bread
wrappers! (This was done to a Duo-Art Grand *while the stack was in
the piano!*)

The worst case was in an Ampico reproducing piano where it's owner decided
to stop any leaking around the unit valves by gluing them to the deck.
Impatient, he had to try the piano before the glue had dried, and the glue
was sucked into the expression mechanism and all the way into the pump!
I said to him: "You did it -- you fix it!"

Bruce Clark