Place the safety in the FIRE position. (This important, if you don't want to go chasing tiny parts). Remove the three small screws, using a 3/32" hex wrench, and carefully lift off the plate.
Result: Marginal improvement. The next step was to buy a replacement sear. Air guns of Arizona has a very nice adjustable one with hardened inserts for $30, but I cheated out and bought a $18.95 kit from Archer Airguns. This was a simple one piece sear that came with three additional washers for removing play from the sear and trigger:
That's it on top. I inserted in the gun, along with the shims:
After reassembly, the long, scratchy, trigger pull was gone, and in its place was a solid, crisp, trigger with no take up at all. Not bad for less than $20.
Unfortunately I did manage to pop out the safety spring and detent ball while doing this! I made a new spring from a Bic lighter spring, but the second time the ball popped out I lost it for good. I'm off to the hardware store tomorrow to look for 3/32" ball bearings.(They didn't have them, so I bought a pack of 100 on eBay. I'm set for a while at least!)