Car stutters and then shuts off after driving 5 or 10 miles?

My car listed above has under 35,000 original miles. It was stored for 30 years before I bought it from an estate. I replaced the gas tank, fuel pump, fuel filter, carb, and cleaned the fuel line. It starts and runs great but after driving a short distance the car begins stuttering before stalling out so I can pull off the road before it stalls and then wait for about a minute or so before it will start back up like normal. I can then drive it again, but it will repeat the stalling process as described. I pulled the plugs, cleaned and re-gapped them even though they did not show any issues. When it is not stuttering, it seems to accelerate and run smoothly. The check engine light has not come on and I have tried loosening and removing the gas cap but that has not made a difference. I have not looked into the electrical as of yet as I usually only drive about 5 miles to the gym or grocery store, so this generally does not happen unless I try to go a longer distance.