In your theory, you argue that Min's viewing of Rand merging with another man, and one living and one dying, makes the body-switch idea problematic/impossible.

First off, I agree with you that the viewing is about Rand and Moridin merging, not about Rand & LTT. There's no doubt in my mind that's the case.

But suppose Rand's body dies while spilling his blood at SG (thereby fulfilling the Aelfinn requirement that he die). But, Rand's and Moridin's souls remain linked in Moridin's body, for a time, due to the "merger" (prior to Rand's body's death, the merger was encompassing both bodies). Eventually Rand wins control of the body, somehow evicting Moridin's soul (thereby fulfilling Min's vision of a merger, with one living and one dying).

In other words, from the Aelfinn's perspective it's Rand who dies, because it's his body that dies. But from Min's perspective, it's Moridin who dies because it's his soul that is returned to the soul pool.

That (or something along that idea) is about the only way I can think of how the body-switch idea can work in conjuction with Min's viewing. I'm not saying I buy into the idea, I was simply trying to think of a way to get around the problem you identified.