We just had an 1/8" thick disc of steel cut to stiffen the timing cover and welded to the front, did a nice job of firming up the part where the button contacts.
The diameter of the disc was sized to be able to weld it onto the raised triangular emboss on the cover.

Still need to mock up the water pump housing to see if there is any interference with the added thickness. Ideally would like the housing to
butt against the weldment.

Joe