IMO, your arguments aren't convincing. In the end, you theory is largely based on Gawyn's announcement that he will kill Rand, while the other clues pointing to a faked death are just red herrings in your view. However, also other characters like the Forsaken, Slayer or Fain want to kill Rand. Nothing indicates why explicitely Gawyn has to be the key player to do it. If Rand really just has to die in some random way for his own good, he could even kill himself just to be ripped out of TAR by Nynaeve later (of course, this additional theory is pretty loony, too, and doesn't explain why Rand is supposed to be alive & dead at the same time). It makes rather sense to me that Gawyn will eventually realize that Rand isn't such a monster and didn't kill his mother.

Finally, as said, you pretty much ignore the images of an important funeral in many of the Prophecies in question and that – according to these Prophecies - the most important characters in this plotline besides Rand will apparently be Alivia, Rand's three girl and Logain, but not Gawyn.