Perhaps I'm missing something here but what's so wrong about the middle seat? At the end of the day what matters when flying steerage is you have ample leg room. I'll gladly take a middle seat over-wing emergency exit seat over a normal E+ aisle or window seat. IMHO the middle seat gets a bad rap, people are willing to do anything to avoid it even if the middle seat is the best available seat.

That being said, I would be checking the seat map like a hawk every couple of hours to see if something opens up. The moment it does, pick up the seat online and/or get on the horn with UA. The best seat should be the over-wing exits regardless. IIRC the window over-wing exit seat is considered an E- seat due to the protrusion of the door. If you could switch to that it would be ideal since you would get most if not all of your E+ seat fee back. Having flown long haul on UA quite a few times it's not a bad seat at all. The profusion can be used to sit your feet on it whilst cruising. In addition, the leg room is ample and you can literally get out of your seat and into the galley without stepping over anyone!

Safe Travels,

James