The separation can be glued.  First clamp the gap together.  Remove the
lag screws and drill for 3/8" carriage bolts.  You want to have a bolt
at least at each vertical post.  More can be placed as space allows.

The reason for drawing the gap tight before drilling is hole alignment.
If the holes were drilled while the gap is open, then the hole will not
be straight when the gap is closed and the bolt shank will be
restricting closure.

Unclamp, clean out any debris, apply epoxy, clamp, bolt, let cure.
A piano tilter makes this job easier.

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