How can I prevent Skyrim from freezing at the load screen?

I recently got Skyrim Legendary Edition for the 360. I started up a new character and everything was going smoothly and I was having a grand old time for a week or so.

Now the game keeps freezing on the loading screen very frequently. I've experienced 4-5 freezes already. There was one time where it froze while I was walking around. The majority of the time, however, it freezes when it is on the loading screen with the tips. The sound will cut out, nothing moves, and the tips don't fade in or out anymore. I can't access the guide either. I have to manually shut down the Xbox in order to get it anything back.

I've looked on forums and tried a bunch of things but none have really helped. I've tried disabling auto-saves as well as clearing the game cache (LB + RB + X).

I don't know if this matters, but I installed the DLC off the second disc first. Then, I installed the main game. When I ran the game for the first time, the patch downloaded and applied. The disk is new too.

Any tips on what I can do? Is my game save corrupted or something? I really want to enjoy this game but the freezing is really making this a less than stellar experience. Any help would be greatly appreciated!