hahaha yes... I got it to work. I don't know if this is going to end up being bad for the tv but it works. I set my xbox to 1360x768, hooked it up, then played with the settings for a few. Once I was done making sure that the resolution I supplied would work, I changed it to 1920x1080. At first it gave me the incompatible signal message, but my xbox screen showed itself, so I got a little confused, canceled the change, and tried one more time.
It did the same thing, so I checked the signal and it was saying 1080p. So, I accepted the change and set it to dot by dot, and it works. 1920x1080 settings in the xbox, and it still claims to have a 1080p input.
HOWEVER, I have not turned off the xbox and set it back up under my tv (I had to use my westinghouse l2410mn to change the settings in the xbox to 1360x768 first, then hook up to the sharp.) I will continue to do a few little tests and make sure this is not going to make the tv flip out.