I have pondered on the subject of the "transposing" piano all day.
I wonder how they were built?  If the keyboard slid sideways, it would
seem that any two keys would slide away from the stickers at the
breaks.  You would have at least three keys that would not work.

You could not slide the hammer rail or the action for the same reason,
unless you had extra hammers at the breaks, and special action brackets
to clear the hammers.  The bass dampers would snag if shifted over one
note.  Maybe a sliding hammer rail with spares?  In that case, you
could not have bridle tapes.

The only thing I can imagine would work, would be constructing special
interlocking keys, in front of the center rail. of the fronts of the
keys could be shifted, and end up interlocking with the backs of the
keys, with a sort of "tongue and groove" interlock for each key, it
might work.

By the way, some of the older player stacks, like the old Apollo that
"played" the keys right behind the fallboard will fit most any piano if
the keys are long enough and the cabinet is large enough to accommodate
it. a stack like this ignores the breaks, and most uprights are pretty
much the same spacing in this location.

Andy Taylor
Tempola Music Rolls

 [ The stickers which contact the capstan screws on the keys,
 [ and the rear tails of the keys, have no breaks in the pattern.
 [ I can't remember the details; possibly the sticker was in two pieces.
 [ -- Robbie