A BIG

and heartfelt thank you to WGH and Zuman for their combined suggestions to use non-wood screws or bolts. I used eight slightly oversized threaded bolts to add even pressure around the gasket. Then, because the driver was being stubborn, I used a claw hammer (with plenty of padding against the front baffle) to 'pop' the gasket free. In my very layman's opinion, the combined pressure from eight bolts and the claw hammer were enough to strike fear into the stubborn gasket that it gave up its fight without so much as a whimper - and there's no damage to the underlying MDF.
All three copper coil inductors snapped free of their zip tie anchors. I suspect that had they also been hot glued to the crossover boards, I would not have this issue. The inductors appear to have unrolled a half-turn, and I'll zip tie them back to their <presumably> original windings before gluing and zip tying them onto the boards. I think I can repair the damage on my own. I can understand why the largest/heaviest inductor snapped free of the zip ties, but the smallest one is quite light. The clever 'three-lettered' shipping company ending in the letter 'S' employee must have gotten creative with his exeriment to maximize the sheer force required to cause all three inductors to snap free of their restraints. I hope he lost his job.
Free beers to all who participated in this driver removal adventure, but ya gotta come to my house to take advantage of my reward, or meet up at Pacific Audio Fest this Fall.