If they release a digital version and it works DON'T BUY IT.
Rockstar will need to solve this problem with a patch or honor those who bought the game with a digital version (if it works). I am not a video game lawyer but if they are unable to patch the game my logic tells me they would not be able to sell the physical game. They will have to remove the physical versions (of Xbox) from the store as you can't sell a game advertized as Xbox 360 when it doesn't play in some Xbox 360 versions.
You're right, morally, I probably shouldn't, but the game is so good I don't know if I could stop myself, especially if it's just a few button presses away. But, heh, that's all hypothetical, for all we know a digital copy might not even work. And you are right on the fact that it should work on all Xbox 360 consoles, they should either replace copies with working ones or replace their boxes with ones that have a huge disclaimer warning customers that it doesn't work on some consoles - and specify exactly which ones. That would require them to pinpoint what the issue is though, and every response we've got so far seems to indicate they just don't care enough to work on it. I hope I'm wrong and people are hard at work trying to figure this out, otherwise we might be screwed.
I just wish Rockstar would stop ignoring this issue, the problem is annoying enough, they're making the whole situation insulting.
I've been reading this thread since page 1 and I was having the same problem, my old xbox is a 20gb pro I've got after the first got rrod'd (OPUS codename from the post above); BUT:
I think a found a working solution that allowed me to play for 3 hours straight!
1. I bought a 32gb usb flash, install the disc 1 there, 2. Install disc 2 to HDD and move your saved game (If you have one) to the cloud, don't let the game save to HDD because I did that and it started giving problems again, just save to the cloud and... well that worked for me.
Try it and tell me if this worked for you!
I tried it with 16 GB USB stick, except I didn't put the disc 2 on the HDD.
Did you try that or anything else before coming up with your fix? Were you driving at full speed through crowded areas while in the game?
I might try your fix depending on your answers, I'm a bit burned out on troubleshooting attempts at the moment.