Just got off the phone with a buddy of mine that's been rebuilding automatic transmissions for twelve plus years, and he suggested that while it may be any number of things, it sounds likely to be a sticky "overdrive valve body" due to the fact that it corrects itself after jiggling the gas pedal.
Unfortunately, there's no way to be sure what is really wrong without taking the transmission out and visually inspecting all the bits and pieces.
If it is a sticky "overdrive valve body," it would be caused by a general build-up of gunk in the transmission, but just changing the fluid (while helpful) won't clean the gunk off of the valve body. He recommended that before you pay to have the transmission torn apart and rebuilt, that you try using a transmission flush/cleaner on it. That will actually clean any gunk or residue off of the parts, and if it fixes the problem, you've saved yourself $1,000's of dollars on a repair bill.
Again, it could be any number of things, but that was his recommendation.
Good luck.
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