And here I am again. I tried my 360 again today, and it has now officially RRoD'd. After cursing it, I figured that at least now there was no doubt. The freezing wasn't corrupt files, or any other such bullshit. I had accumulated around $300 of cash I've been putting in a drawer as play money, so off I went to Best Buy. Got an arcade unit, Jasper chipset. They have a deal for a free game if you get one of those, so I got Fallout 3 GOTY and Batman Arkham Asylum. $60 off that put me at around $255 including tax, which I just realized means one of the games at least cost less than I thought. Either that or there's some other discount in there somewhere. (It should have been $260+tax.)
Got it home, hooked it up (150-watt power brick for final verification--yay!), and now I'm transferring licenses as in my above post. Unfortunately a couple of things so far want to redownload from scratch, including Shadow Complex. To make matters worse, their servers must be getting hammerer, because it's slow going. I ended up canceling out of Shadow Complex, which means I probably won't be able to play it at all until I decide to bite the bullet and wait for all 835 MB. I don't know why the hell the transfer can't be applied to everything without going through this bullshit, but at least it's doable.
The unit comes with a wireless controller, itself around $50 on its own, so really, it's not too bad of a hit to move to a hopefully more reliable chipset. We shall see. And I'll finally get to try the wireless controller, which I've been actively avoiding because of my hatred for batteries.