To answer the poster's questions:
(1) You say that the water drains from the tank when you turn off the water supply to toilet? If so, then he hasn't fixed the flush valve yet, maybe just made it leak much more slowly. Also, depending upon how low it goes, you might want to check and make sure that the copper pipe that goes from the fill valve into the overflow riser isn't stuck way down in there, because that can siphon the water out of the tank through the fill valve.
(2) You say that it continues to rise past the optimal water line and up and over into the overflow riser. This means it isn't shutting off or shutting off enough.
Solution to #1. Fix the flush valve, after testing to make sure it isn't cracked and leaking anywhere other than around the flush ball. The overflow riser and/or the base of the flush valve could be cracked. If so, it should be replaced or the crack soldered. If it's just that the flush ball isn't sealing, either fix the flush-ball-and-wire setup, which any halfway-competent plumber should be able to do, or replace the flush ball with a flapper (Korky Model 2000bp, for example) that works on Douglas flush valves, assuming that it fits.
Solution to #2. If this plumber has ever adjusted a real ballcock before (and not just replaced it with a Fluidmaster 400A because adjusting the ballcock required too much skill), he should have no trouble adjusting the fill valve in that toilet. It isn't rocket science. The ball rises on an arm, and, just like a bottom-mounted ballcock, the rising ball lifts the arm and the lifted arm operates a valve which stops the flow of water. There are a couple of different designs, i.e. diaphram-style and piston-style, but they all can be adjusted. Seriously, if he can adjust a Wolverine Brass ballcock, he can adjust yours (or replace or repair it if he hasn't already).
The company that sells the Scovill fill valve that I showed above includes instructions for installation and adjustment with it. If he has thrown those away (or hasn't replaced the fill valve and it just looks pristine to me), then try calling them and see if they will fax you or email you the instructions. Then tell him to put on his glasses and read them. Then everything should be fine.
Let us know as this proceeds, as we're eager to see some more photos and help you towards a positive result.