The first thing to make sure of is that the blocks that the back
casters go into have not come loose and shoved up.  If the wood they
go into isn't sound, no caster will work well.

I almost always use the Schaff 4588.  If the old ones were the Schaff
589 style you may have to drill the holes deeper but the wood bushings
will make the sockets solid.  I put some glue on the outside of the
wood bushings and put them in the hole than drive the socket in.
Quite often the wood bushing splits but since it is tight in the hole
it doesn't matter.

If the old casters are the Schaff 4588 style and the old sockets are
solid, sometimes you get lucky: all you have to do is pry the old
caster out of the sockets and shove the new one in.

As for steel vs. rubber, I feel that would depend on how much you
intend to move the piano.  If you are someone who doesn't even allow
dirt in the flower pots and are going to move the piano to clean every
week I would use rubber.  If the piano is only going to be moved once
every couple of decades I would use steel.  Rubber is easier on the
floors but will flatten if left in one place for a long time.

If floor damage is a concern and the piano is not going to be moved,
you might want to consider caster cups such as the Schaff 838 series.
Try to find ones with a flat bottom area where the caster rests, not
a dish-shaped bottom.  With a dish-shaped bottom the whole weight is
where the edge of the wheel makes contact, instead of being spread
across the entire width of the wheel.  This can cause a dish shaped
bottom to split over time.

John Dewey