but couldn't fit it in logistically????

Here is how you fit it in. You have Perrin find Faile earlier, or you just don't have Faile go missing AGAIN (hasn't Perrin been searching for her enough in this series? Did we really need him to have to search for her AGAIN???).

Once the Faile issue is cleared up, I could see a scene with Rand leaving his tent, walking by another tent close by and hearing Mat and Perrin talking, and he walks in to the tent.

Switch point of view to Perrin, with him and Mat smoking their pipes and remembering their friend (they are not at the "funeral" because they would rather be alone at this somber time).

Before Rand walks in, Perrin smells someone outside, someone who smells like Rand. "Moridin" walks in and of course Mat jumps up and freaks out, and Rand with his new special powers knocks Mat's hat off or knocks him down to a sitting position. Of course Mat will be freaked out even more because his medallion should stop someone from channelling on him. Perrin, meanwhile, is laughing because Rand's "smell" transferred to his new body (the smell is something of the soul, not the body I assume). Then they chat for a couple pages after Mat realizes what is going on. Then Rand leaves the tent. The End.

How hard was that?