My gut feeling is that when Rand lives again, it will be under the following 2 conditions:

1. Only a very select few will know Rand lives. The general population will believe that the Dragon Reborn died (for good!) during the Last Battle.

2. After living again, Rand will look substantially different than he does now.

#2 is needed in order for #1 to be true. If Rand lives again looking like he does now, too many people would recognize him, and it would eventually become public knowledge that he survived. I don't think that will happen, so ...

And, I don't expect him to live on as a recluse; if he's to be Elayne's part-time husband, he'll be a public figure (more or less). But no one outside the select few will know he was the Dragon Reborn, because he won't look like Rand.

The "body-swap" theory can satisfy both conditions, but there are a few DFs who know what Moridin looks like (and presumably some of them will survive the LB), and if they see him as Elayne's husband (say), it could be problematic.

The "ripped-from-TAR" theory wouldn't satisfy both conditions unless Rand looked different after he was ripped from TAR. Some people have suggested he could look like LTT after being ripped from TAR. Based on my (admittedly limited) understanding of Heroes in TAR, I don't see why that would be the case, but it's possible I suppose.

At this point I'm not married to either idea. But at least they could satisfy my 2 conditions, whereas other theories I've seen cannot.