I have replaced the casters on quite a few player pianos.  In the shop
I use a piano tilter.  Before raising the piano with a tilter I find
it a good idea to raise the piano and slide a 2x4 board under it going
front to back and missing the casters at each end.  When setting the
piano back on its feet either slide the piano towards the handles of
the tilter enough so that you can put a 2x4 between the bottom of the
piano and the prongs of the tilter or have the 2x4s on the floor so
that the piano will end up standing on them.

The reason for this is that as you raise or lower the piano if the
back casters touch the floor when the piano is tilted they can cause
the piano so slide off the tilter prongs and go thump flat on its back
on the floor and send the tilter banging against your legs.  It takes
a fair amount of strength to get a player piano back up on its feet
when it's laying flat on it's back under a work bench!

In the home I have used my tilter or, if the ceiling is high enough
and you have enough manpower, you can tip the piano up on its end.
With the piano setting on it's end you have access to the casters.
I suggest putting a moving pad or blanket far enough under the end of
the piano you will not be lifting so that it is under the casters at
that end and sticking out far enough so that it will protect the finish
on the end of piano when it is on end.  The pad will help keep the
piano form rolling on the casters while you are picking it up and
letting it down.

If you just jack the end of the piano up far enough to lay on the floor
and have access to the casters, make very, very sure you have a very
sturdy block under the piano, going all the way from front to back,
and only do one end at a time.  Remember that upright pianos like to
fall over on their back.

Some of the time you can just pop the old casters out and put new
casters in the existing caster cups.  If you do this make sure the
caster cup screws are all tight and solid.  Longer screws may be a
option.

If you have to replace the caster cups you may find the hole is larger
that the new caster cups.  Schaff Piano Supply sells a wood bushing that
you can put in the hole to make a tight fit.  You may have to drill the
hole out some if you use the bushing.  I like the cup and bushing to be
a tight enough fit so I have to drive the cup in with moderate hammer
blows.

You also may have to carve out some of the wood around the caster to
make room for the new casters to pivot freely.  Remember once they have
weight on them they can push in some.

John Dewey