My guess is there is only so much that can be done to correct the problem and the locksmith did the best he could with what he had to work with.
That said, IMO, no good locksmith would do as I'm about to suggest.
I would remove the frizzen, springs, tumbler etc.
I would then lightly file the top surface of the pan to make sure it was clean, bare metal.
Then, I would heat the pan with a propane torch with its flame set about as low as possible.
After fluxing the surface with an acid flux, I would carefully build up a layer of soft solder on the entire surface.
With soft solder, there is a narrow temperature range where the solder will become soft and can be applied rather thick. This is know as the solders "solidus" range. For 50/50 solder it is between 361°F and 421°F. At 421°F the solder turns into a liquid.
With the solder in this temperature range it will adhere to the other solder so building its thickness up is possible.
(By the way, the 80Pb-20Sn solder is what was once used to "lead in" auto bodies. Its solidus temperature range is between 361°F and 535°F giving a much wider temperature range to work in.
We used to build up layers of it and actually push them around with a wooden blade to form and smooth them out when leading in custom car bodies.
It might be found at some of the old fashioned auto body or custom auto shops.)
This will take a bit of patience but I would try to build up at least 1/16" thickness of solder over the entire surface of the pan.
Once done, I would refit the frizzen with its screw and begin the slow task of using a transfer medium like in-letting black to find the places where there was interference with the pan lid/frizzen and slowly filing away the excess solder.
If all goes well, I will end up with areas where all of the solder has been removed and other areas where a thin coating of solder remains. (The fact that there will be areas where all of the solder is totally removed is the reason I would not try to use the brass shim method).
Because it's impossible to blue or brown solder I would leave the entire top of the pan in the white.