The only time I have ever had that error on my Xbox was with Oblivion GOTY edition and it was just because there was a big smudge on the disc, cleaned it and it went away.
Since it worked fine in another Xbox I would think it is your Xbox dying.
But, you say it runs fine with other games so that takes us back to Skyrim.
You said you did not have this problem until 1.9 and you have frequent crashing..
Have you tried cleaning your Xbox system cache? If not try that, if that doesn't work then try uninstalling and reinstalling everything having to do with Skyrim. There may have been some kind of error created during install that is corrupting during load... If that doesn't work, I don't know.
I am not super-techy like some other people on these forums so you may get a better response but everything I just stated above would be what I would do if I knew for sure that it wasn't a problem with my Xbox dying or the disc and from what you explained it doesn't sound like that is the case since other games work and your Skyrim disc works on other systems.
BTW, occasional and even constant crashing is a issue that many of us have suffered since 1.9, it seems like clearing your system cache or game cache on a regular basis seems to help it quite a bit.