Bitter

+1 on the gas filter. I had a car with similar symptoms (loss of power that went away after stopping and restarting) and the filter was the culprit. With the low mileage you have, it's entirely possible it sat for long periods and the filter is gummed up from old gas. It's relatively inexpensive and easy to replace even if it turns out not to be the problem. It probably wouldn't hurt to add a little Seafoam to the tank as well.

Nuke

The only other thing besides the TB that comes to mind is the chronic water leak (there's a TSB on that, definitely) which begins to cause connections on the Smart Junction Box to corrode but I've rarely if ever heard of it causing ONLY drivability issues. The SJB is located inside the front passenger kick panel. Sitting in the rain, water drips down and into/onto the SJB. The corrosion causes all sorts of electrical gremlins and it's not too far fetched to imagine the SJB erroneously telling other sensors that something is amiss. The water leak was very common with the 05's and 06's and Ford's "fix" beginning in '07 was a little plastic "awning" over the SJB. Yep, my DOG could have figured out something better.

If the car sits in the rain, grab a tissue and see what happens when you blot the carpet at and under the kick panel. The SJB might be a shot in the dark since they haven't been able to figure out what's going on.