How to clean gunky CDs

Years ago Cd's in box sets used to be packed with foam inserts holding Cd's in place. I probably should have removed the inserts at that time because now I find that some of them have deteriorated to the point where they leave a sticky substance and bits of foam on the non-playing side of the CD.

I have tried plain soap and water, alcohol, and even lighter fluid. Nothing removes this gunk and I don't want to insert the CD in my player and risk gumming up the mechanism. Any recommendations as to how to remove this gunk would be appreciated?
Try a good plastic polish
Not a recommendations, but a if all else fails...Perhaps putting the cd in slightly less than boiling water then scrubbing with dish pad used for non stick pans.
Please post your results.
Try Goo-Gone, a citrus-based cleaner that seems very good at removing gummy residues. Also, you might try some Scotch packing tape. Give it a minute or two to adhere to the goo and then pull it off the CD. I would try both of these methods on a CD I didn't particularly care about for starters.
Acetone, sparingly dampening the cloth.
Whatever you try, do it first on a blank CD or a CD you don't care about, particularly if you're going to try a solvent as powerful as Acetone.

I, too, would have recommended Goo-Gone or one of the similar citrus based cleaners. WD-40 dissolves some kinds of adhesives and might be worth a try. You might combine the solvent with a Magic Eraser pad, followed by a good plastic polish.

Test first.
Acetone? That will melt a CD. It dissolves the polycarbonate. Isopropyl or methanol (limited contact) will work.