Can you figure out enough about what the pickguard is made of to consider the possibility of re-flattening it?

As long as you're not doing anything with it while you're looking for an adhesive, putting it between a couple of big books and piling on a stack of books for a few days might give surprising results - if it's an artificial (plastic) material.

Even if it is a natural product like real tortoise shell, careful compression on a slightly compliant surface (i.e. between a couple of books or smooth boards) shouldn't be harmful. Since I've never seen a turtle with a big truly-flat shell, if it's made of real shell (or unrolled cow horn etc) it was probably mechanically "formed" to begin with. The original process for an animal material may have used heat and/or solvents for softening to allow fairly extreme bending; but for minor corrections those shouldn't be necessary.

John