At first I thought that this problem was either my imagination or something simple, like condensation in the tank. But I've had the problem for a couple of months and many fill-ups under varied conditions...
Whenever I fill up my tank (normal fill-up: wait until the pump clicks off, then give it one more squeeze until it clicks off again), my engine and IMA behavior changes. For the first 20 miles or so on a full tank my MPG is great (50-60 mpg average), the engine seems to have more power, and the IMA seems to kick in more often (keeping the MPG higher). I can also feel the difference in power, acceleration, etc. Its like my car has an extra 15 HP for a few minutes AND better MPG. At the same time, it has a pretty bad "stutter" randomly. As if it had a badly clogged fuel filter or something.
However, after about 20 miles, the power slowly drops, as does my MPG, and the "stutter" completely goes away. Under "normal" conditions, I'm getting about 42-43 MPG, and power seems fine, so I'm not complaining about the state of things for the 99% of the time, but I can't figure out why it runs so good for that first 20 miles or so then drops off so dramatically.
It acted the same way while I was on a road trip, so the same problem occurred every time I filled up no matter the time, place, altitude (Colorado, California and places in between).

Things I've tried:
different gas
different octanes
fuel additive
new spark plugs
new gas cap (happened to have a new Honda one)

No warning lights are on, and the car has a new IMA battery that functions perfectly (thanks to Mile Hybrid).

Specifics:
Under normal conditions, my IMA will kick in when the MPG gets down to 20 MPG or so, sometimes it'll kick in at around 35 MPG. Immediately after a fill up, however, the IMA will kick in ANYTIME extra load is placed on the engine, even if the MPG is around 40-50 MPG. It's very smooth, as if the car is worked perfectly right after a fill up, and only at about 85% the rest of the time.

Does anyone have any idea what would cause this type of behavior? I'm totally stumped and any searching I've tried has come up empty.

UPDATE:
I've tried several different combinations of gas, gas stations, driving habits, drivers, etc. This is the end result: The car/engine/IMA/computer all run better on a full tank for about the first 50 miles or so, with a noticeable drop-off thereafter.
Sometimes this period also includes the previously mentioned stutter, and sometimes it doesn't.
What would make the fuel system and/or computer behave differently on a full tank? What changes after the first little bit of gas is gone?
Has anyone ever heard of a fuel pump making a difference in MPG?

Thanks