And of course if you don't shuffle Inn into your deck with Inn's own power, you can still reveal Watchtower to top-deck Inn after you've shuffled, and Isotropic correctly allows this.
Now this I didn't realize! So you can in fact use Watchtower to end up with an Inn on top of your deck? I always assumed that it was impossible; Inn would either be shuffled into your draw deck or left in your discard. I guess it makes sense, that "lose-track" doesn't actually happen here; but I always thought it would. You gain Inn; then choose Inn's reaction first. This allows you to look through your discard pile and pull actions out of it. Even though Inn doesn't actually move to another place because of this, your discard pile is being manipulated; to the point that I thought Watchtower would lose track of Inn.
The difference, I think, is that the discard pile is face-up (and also is known to contain the Inn). You can't shuffle your
deck and then top-deck something that you shuffled in, because you don't know where it is, because the deck is face-down (and you're not allowed to look, hence Stash requiring a different back).