Glenn,  This may be a long shot, but have you considered dismantling
the piano and taking the plate to a foundry to be recast?  The plate
itself can be used as a pattern for a new one, although the foundry
will have to do some "tricks" to make it work.  (E.g., first fix the
bowing, and then add material to account for the shrinkage that the
iron does while cooling after casting.)

What I find odd is that the plate is continuing to move; moisture
doesn't usually cause cast iron to move -- but rust, yes!  A 3/4-plate
does rely on the integrity of the wood back more than full plates:
the wood back is actually part of the plate, the iron merely being
a stiffener.

If you have the plate recast, you might consider having parts of the
web made larger, so as to be more stiff.  I suspect that this process
would probably not be greater than trying to transplant a different
piano into the Orchestrion.

Sounds like a fascinating project!  I hope other members of this list
can expand on my thoughts here, just so long as they don't call in the
padded van with those guys in white coats!

David Dewey