1986 Buick Century EGR Problem? (long)

My 1986 Century sedan with the 3.8 litre roller-cam engine (VIN character "3"; multi-port fuel injection, distributorless HEI, California car) has a problem
with hesitation (misses, stumbles, coughs, very slow acceleration) when accelerating from a stop. I took it to my Buick dealer for a diagnosis and all he could tell me was that it's "something wrong with the EGR circuit" and it would probably cost about $400 to fix. Since I'm very familiar with the car after doing a lot of my own work on it in the 13 years that I've owned it, and I'm trying to sell it for maximum recuperation, I thought I'd give it my best shot, but I'm stumped.
It runs fine at idle and at all speeds above about 5-10 MPH. With transmission in gear and brake firmly applied, gradually pressing the throttle results in engine accelerating a bit at first, then as throttle is pressed farther, engine begins to stumble and can be stalled by pressing still farther. I've swapped the EGR valve itself (both the removed and the replacement EGR check good with a hand vacuum pump) and the solenoid control valve, with no change in performance. Disconnecting the vacuum line at the EGR improves performance considerably but not 100%. For reason unknown, the ECM seems to be commanding premature/excessive EGR valve opening. Of course there's no ECM trouble code being set.
In all the time I've had this car, I've built up quite a collection of spare parts. Here are some other items I've swapped recently with no improvement to performance: MAF sensor, ECM, coil & ignition module pack. I also checked the throttle position sensor, which seems fine. Note that all the swapped parts were used (including the EGR valve and solenoid), so they're not completely ruled out, but IMO at this point very unlikely suspects. I did some reading about how the EGR system is supposed to work and such things as the vehicle speed sensor, coolant temperature sensor, and knock sensor were mentioned; could one of these be the culprit?
The last major headache I had was intermittent stalling/non-starting (also with no trouble code), which after visiting 4 shops including the above mentioned Buick dealer, was found by a Firestone mechanic on his second opportunity to be the crankshaft "dual sensor". The new hesitation problem doesn't seem to be related but I thought I'd mention it just in case.
I prefer email replies (see below) but will check back here.
TIA for any help you can provide.
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Alan "A.J." Franzman
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