Oh, well.....out came the power screwdriver, and THIRTY FOUR screws later I had it apart.
Oh, and they were all slightly loose, allowing 33 years of road dust to collect in the void spaces where the two pieces screw together. Took about 20 minutes to brush and vacuum it out of there.
So I then sanded off all the old gasket residue stuck to the fiberglass, as seen here in before and after pix:
It actually went easier than expected. I used a flexible block like a sponge, coated with "220 grit" abrasive, and took my time. It's a bit like hand finishing wood in that you carefully watch the amount of material being removed, and STOP when the stain/imperfection fades away.
This also breaks any sharp edges, and might prolong the life of my low-buck replacement gasket. Sharp edges pressing firmly against soft material usually results in soft material losing.
And then the fiberglass spoiler starts rubbing directly on the paint, and paint loses, too, as seen by the orange lines of rust on the hatch where the OEM gasket had been completely compressed, and then cut through, by the spoiler.
So now I have to bust out the Dremel, and use one of the small felt buffer pads to clean out the wells the screws live in. Luckily it's just fossilized road dirt, so it should "Buff Right Out" using mild cleaners.