After reading the WOT , I had gotten the feeling that RJ was a church going man where other authors I didn't get that feeling from their writing. After reading RJ's blog and seeing the pictures of his funeral, I believe him to be a religious man. That's why I doubt that there will be a polygamist ending because it would fly in the face of his beliefs.
True in some cultures polygamy is practiced, but polygamy in America is rare and at best taboo. Pretty much anyone who has dated has dated someone who has cheated on them. I think that some, especially the female readers, may find a polygamist ending to be a bitter pill to swallow. In today where political correctness and hyper-sensitivity runs wild, I think that ending very well could be seen as RJ endorsing polygamy. Which could cause some readers to turn away from RJ and not buy anymore of his books.
When RJ was telling the ending in his living room to family and friends shortly before his passing. I don't see him ending with Rand, Min, Avienda, and Elayne all getting married and living happily ever after, I don't see Harriet standing and clapping her hands. It would also go against the overall theme of the women in the book that of the strong independant female. Lan could have three wives and get away with it, but not Rand.
The little that I know of RJ tells me that the overall character of the man would not let him write that ending.
Lews Therin talks to Rand, but I believe if my memory is correct, there is a third unknown voice also. Assuming that all three girls are former wives, perhaps somehow Rand gets split in three? This is the only way that I can see it working. The unknown voice would go with Avienda, Lews would go with Elayne (her name is to close to Lews wives name to ignore), and Min would go with Rand.
If you really want a happy ending then lets say that people die, and Rand gets split. Instead of all the people fighting in the same age, Tarmen Guiden is fought in all ages. So Lews would go back to the Prologue and get a chance to save his wife who'd be Elayne, at the same time that Rand fights to save Min, and the unknown voice would fight in the Wastes and saves his wife who'd be Avienda. After the battle mass resurrections ensue. What would Mat, Perin, and everyone else have to do with everything? I don't know....perhaps their just there for the pre-battle before Rand splits.
That's the only scenario that I can think of where Rand and all his wives live.