Miller,
I went out to the shop and pulled the front wood off the gun, and double checked the screw, tightening it down. Sure enough, it clamped the plunger down tight. I figured I'd take it down one more time and polish things up a little to see if it helped.
On the underside of the plunger was a circular half round chip of steel, compressed and rusted into the plunger. I am sure it was debris from the manufacturing process, and the damn thing was nearly invisible! I scraped it off, and polished and lubed everything and re-assembled. WIthout that chip there, everything is exactly as it should be. Glad I looked a second time, thanks for getting me thinking about it a little harder.
The screw is tight, now. I guess I could do worse on an old grouse gun.

Best,
Ted