Brian,  You can do one of two things or a combination of them.  The
easiest would be to lower the plate (considering string height and pin
block elevation/angle) to gain proper downbearing in that area and shim
under the rear bearing bar felt for the rest of the piano.

Option two would be to install a new bridge cap in the section to gain
height.  Depending on the degree of the warp, a little of each might be
used.

I would not thin the plate for fear of failure along the hitch pin
line.  You could grind down a bearing bar if there is one.

You did not mention the make or type piano, but the negative
downbearing has damaged the bridge pin holes, so either recap or swab
the holes with epoxy and install new pins.  Most false beats emanate
from loose bridge pins.  Replacing the pins is a good idea anyway
because over the years the wire has put a notch in them.

Remove all pins, sand the bridge surface flat to just remove the high
spots, swab the holes with epoxy and let cure.  This sizes the holes
and reinforces the cap.  Ream the holes for new pins and renotch.  (By
sanding, you moved the terminations out from the center of the pins).
Use CA glue as a pin driving fluid; this will aid in making the pins
rock solid.  This procedure greatly improves the termination at the
bridge.

Regards,

Jon Page,   piano technician
Harwich Port, Cape Cod, Mass.