Yeah, an interesting situation!
In our last game, I remember that even though I had the
Mount Doom from region 2 under control, it wouldn't allow
traveled leader to change the sites that were in region 2.
That's pretty straightforward, as the card states "until the
end of the game" as a BOOM once the card is played that's the issue for the rest of the game. So even though that
Mount Doom wasn't in region 2 anymore, since it was controlled, the fellowship and the subsequent sites they were at were still in region 2.
I looked through the rule book and current rulings, but couldn't find anything addressing this situation.
If I had to GUESS, I would say that "exchange" and "replace" should be considered the same thing here. For example: even if I already had control of
Mount Doom from site 4, but the opponent's fellowship was still in Region 2 at site 6. If I were to try to use
Uruk Cavern striker, even though it's technically saying that I am "exchanging" the site with a site I control....isn't site 6 STILL being replaced if that happens? It's just being replaced by a site I control rather than one from the adventure deck (a more common scenario).
I guess that one should still be kind of obvious....maybe haha...
But it sounds like you suggested that perhaps the fellowship was in Region 2, site 4 at
Woody End or something, and I already controlled all of the Region 1 sites (one of which is
Mount Doom).
In this case I THINK that I would have the liberty to exchange
Mount Doom or any of the other two sites with
Woody End, because once those cards are under my control, they are "region-free" right?