Although they're burnished in, the burnished section can be straightened. A very fine blade is worked around the edge several times lifting very small sections at a time. On reassembly they are simply burnished down again.
If you cut the burnished section off the group can be epoxied in place, simply running a small bead or a few drops around the edge.
I've always used Acetone to separate elements but am going to try lacquer thinner for those more persistent jobs.
To the OP don't separate the elements in place, You're going to need to remove them to recement them. I use an optical cement available at my local hardware store, I believe the brand is "Crystal Clear" it comes in a small red syringe & is a UV cured glue. Sunlight or florescent both work.