It's more about tautness than wrinkles though they are somewhat related given the stretchy material.
I didn't mean the small wrinkles under/adjacent to the tape; I meant the long waves of loose material running more or less parallel to the ridgeline, the same thing you're calling tautness. In my mind, those are also "wrinkles", though I'll do my best to eliminate both. It definitely will be a challenge to keep out the small wrinkles. That's part of the reason I've been taking so long; I've been going slow and being very careful. I've actually been lining things up a tiny bit at a time and temporarily taping it up with office tape, which pulls off without leaving damage. Once I've got enough small pieces of office tape patched on to one side of the seam to hold it all straight, I turn the whole thing over to put the permanent tape on the other side. Then I flip it back to the first side, remove the office tape, and re-tape with the permanent tape on that side as well.
Thank you for all your advice on this topshot. Since I'm doing this all by the seat of my pants, your input has been invaluable.