If I understand your plan, you are intending to attach both your side plate and the lock to the brass insert with machine screws. Bear in mind that the frizzen spring probably covers the head of the machine screw on the lock side, so in order to remove the lock, the frizzen spring would have to be taken off first. And the machine screw on the lock side would have to be countersunk so the head is flsh with the plate. Do-able, but awkward.
May I suggest a hook on the inside front of the lock plate engaging a screw head in the mortise in place of that front lock bolt. Then a single lock bolt into the plate's bolster would hold everything firmly. A simple washer or inlay would replace the big two-screw side plate common on the Bess.