I created an account just to help you out. I had the same problem, it would get stuck, n upon restarting the ps3 the disc would not be detected and the cd rom would make weird noises, I formatted my console n did everything but nothing worked, I hadn't played gt6 for a month because of this. Most said it's a lens failure, but apparently, deleting bgm files from gallery(next to the garage button on home sccreen) fixed it and I haven't had any problems so far today. So I am led to believe it is a software issue that GT6 is causing, because once I reformatted my console and played a little without updating gt6, it was working fine for the few hours I played it.
Hope it helps you too, let me know.
Update: The game got stuck only after 8hrs of continous play. I don't play anything else on ps3 but my little cousin the other day played fifa n it worked fine, so maybe since there have been so many updates to gt6 it has become heavy on the console. I just finished cleaning the lens myself, I believe this would solve it rather than changing the whole blu ray rom. Dust is always an issue.
I'm not spending 70 more dollars on a rom when all i do is play gt6 on it because they are too lazy to make gt7 for the ps4