Before guessing at the problem, I would like to state that I am NOT the professional that rebuilt the carb; so have no axe to grind.
The carb doesn't care if the truck is in first gear or fourth gear. Sounds like the carb is working if there is fuel in the carb.
There are two possible conditions (that I can think of) in the carb that could cause the problem:
(1) sticking float
(2) use of the "2-ball" fuel valve
The fact that the carb is able to catch up with idle probably eliminates (1). As to (2), I thought the company making those things was out of business. Hopefully, your professional did not have one of these valves on the shelf and used it. I would suggest asking.
So basically, the symptoms point to the fuel delivery system. Possibilities in the fuel delivery system:
(1) new fuel pump of off-shore manufacture, even if in a Delco box.
(2) clogged fuel filter
(3) rubber fuel line
(4) cracked fitting in fuel line
(5) missing or partially clogged tank vent
Discussing:
(1) have personally had virtually nothing but trouble with new auto parts for older cars coming from the other side of the world. (Opinion) rebuilding the original is better.
(2) I read that you changed the fuel filter. Same answer as above.
(3) You stated new rubber fuel line, but not how much. The only rubber should be a "vibration" joint from the frame to the fuel pump. Too much rubber can collapse from vacuum.
(4) A cracked or loose fitting in the fuel line before the pump won't leak, as it is not under pressure, but can suck air under vacuum, thus reducing the output of the pump.
(5) A missing or partially clogged tank vent will not allow air to enter the fuel tank as fuel is pulled from the tank, eventually creating a "vacuum lock" on the tank. Do not know one way or the other on your truck, but many older vehicles had the tank vent as a hole in the center of the fuel tank cap. New production caps, as a rule, do not have this hole.
So where to start?
First, a call to the rebuilder to see what type of fuel valve was used. If the two-ball valve was not used, then just try another new fuel filter (cheap, and fairly easy).
Next, as Jerry suggested, a fuel pump capacity test.
Next, with the aide of a helper to listen for escaping air, try blowing low pressure air from the suction side of the pump back into the tank to locate the tank valve or a possible leak in the fuel line.
Jon.