I do the tape thing that AnimistDragon mentioned, but I use Scotch Magic Tape instead. You don’t have to cut it, and you can easily remove it without damaging the disc.
As a side note, the only game using the tape didn’t fix is Super Bust-a-Move 2. Never figured out how to get that one to work.
Back when I first started having this problem, they weren’t fixing it for free, so the tape was my only choice. That’s awesome that they’re fixing it free now, I was ready to swear off Sony products altogether back then.