have you taken a look at the wires going to the fuel pump?
The whole "acts up on hills" routine smells suspiciously like a carb'd car with a clogged fuel filter.
My ghetto troubleshooting skillset says (if those wires look ok) to toss a whole quart of marvel mystery oil into the gas, since that seems to lubricate senders and pumps (and gets sticky senders back to normal) and see what it does. The stuff really does work in that application--it also seems to quiet down pumps a little. Have you taken a fuel pressure reading yet? Maybe on a steep incline? My personal experience--as riduculous as it may sound--is that a new fuel filter can add an extra 10 PSI (on a ford taurus) of pressure after the car had been run out of gas.
Additionally--and this is a long shot--have you checked to make sure that the alternator is operating correctly throughout the range of speeds? I'll take the back seat up and run some wire to the passenger seat and connect it to a DVM; the whole "cut out at certain rpms" suggests--at least to me--that there might be a supply issue. I know that when I tried to get home after one of my alternator brush springs got soft, the fuel pump would only work under certain rev positions and I had to kill everything electrical in the car to stop it from misfiring (I'm assuming that the FP wasn't getting enough juice in that state).
EDIT: Hell, you could forget all that and simply run some jumpers from the FP electrical supply to the passenger seat, have someone else watch the meter, and try to re-create the conditions under which the problem occured. That way, you'd know if there was a certain point in which the pump voltage went to crap, and work your way out from there.