Elayne was not there when Morgase disappeared, and Gawyn believes that Elayne is being manipulated by Rand, which just makes him even more angry. Anything that Elayne says to try to convince him will just feed that anger, just as Min telling him that Elayne loved Rand fed his anger at Dumai's Wells.

Just as Gawain's sense of honor led to the breaking of the Round Table, and King Arthur's death, Gawyn's sense of honor will lead to Rand's death (in a totally different way, but the same at the core). This is foreshadowed all through the series, and I find more evidence every day. Egwene hasn't actually seen Morgase, and no one knows she is alive except for Perrin and Galad and Rand. Even Mat doesn't know, because Mat and Perrin only see Rand. Why is the Pattern holding Perrin in the south? Why was it so important for Mat to go to Caemlyn before Ghenjei? It all fits together.

I believe that RJ is writing essentially a classic, ironic tragedy that will have a happy ending. The Arthurian bit is the classic tragedy - mixed and matched with other things, of course, but Arthurian at its heart - and the Jesus bit is the happy ending (and it also ties into Arthur). Just as Jesus' death was significant, Rand's death will be significant in that it will gain him the belief of the people. Like Herid Fel said, 'belief and order give strength'.

It could all be a red herring, and if it is, I won't cry. Foreshadowing is good stuff like that; either hint or red herring, RJ left a complex trail of goodies.