I have a 1970 Corvette, automatic THM400, with a the base engine 350cu/300hp. Car went through an extensive frame-off restoration with most everything new. Got the car back last Nov.

Bought a used Quadrajet (#7040202) and sent it off to a reputable quadrajet engineer and he rebuilt it and tested it for 2 days on a test engine.

I drove the car 600 miles when I picked it up last Nov, and it ran great. No issues all the way home. Had to put it away for the winter. ( I put Stabil in the tank for the winter, but not sure if I'll do that next year, I've heard it could cause issues).

To my issue... when I was driving it locally (5-10 miles) I didn't see any problems. Then I went on a longer drive with buddies (40-50 miles), and noticed that going up a hill (under load) it's as though the engine was missing power and sputtering. Later taking off from a red light to turn right, it stalled. Started right back up, but had to feather the throttle. So this happened a few times on this drive. The next day or a few days later, drove around town, and did not encounter any issues. The guy that rebuilt my carb, said that it sounds like a problem with the accelerator pump. And I do remember a few times when I checked the carb, and pressed the throttle that the jets were not really shooting a constant stream of gas. So I changed the accelerator pump, and when I checked the jets it seemed to be streaming a constant jet of gas, so I expected this was the issue.
Took it on another long ride with buddies (50-60 miles), and it ended having the same symptoms. From a stop, pressing the accelerator, it would stall, and once I got rolling and "stomped" on it, it would sputter.
The next thing I changed was the fuel filter thinking that maybe there was an issue. It is one of those fuel filters with a little check valve inside, and when pressing the valve I could feel a little resistance sometimes... replaced it with another filter which does not have a check valve, and took it out last night on a 20-30 miles ride on the highway (60-70mph), and I thought it was resolved as it didn't seem to sputter when accelerating, but as I was taking the exit to get home, the symptoms came back... from a stop, if I pressed the accelerator it would stall, and "stomping" on it, i could feel it sputter and hesitate.

Just wondering if anyone has any ideas of what else may be the problem... as mentioned, if I'm just driving locally around town, it doesn't appear to have the issue, but if I take it for a longer drive that's when it starts.

Anytime it would stall, I have no issues restarting the car, it restarts fine, but as soon as you press the accelerator it stalls.