Scott, you may have fuel in your fuel filter; but is it enough? When you're running the engine up "no-load" (not pulling the car around, just revving the motor out of gear), you've got enough fuel delivery; but when you're driving along going through the gears; then engine uses a lot more fuel, probably more than it can feed itself in this condition.
-That's pretty simple, I know; but I haven't seen it actually
mentioned in this thread! You'd be surprised how easily the simplest stuff can get past somebody when they're frustrated.-
I'd bet a couple of bucks that the clutch/tranny isn't even close to the issue. Pickup filter, fuel pump diaphragm, maybe a vacuum leak. How long did this car sit around -collecting crud in the tank (and carb float bowl) and dry-rotting its rubber components- before you got it?
EDIT: Oh, duh! I just went back and read your posts. 6-year restoration.

Sounds like I was luckier than somebody for once.....When I bought my F100 lots of years ago; it had been sitting in the southern Arizona (Tucson) desert for two years, only was started
once in all that time. I got an entire 10-1/2 months use out of it before all the 'hidden" rubber drivetrain components (fuel pump, carb seals, distributor vacuum solenoid, valve stem seals, oil pan and valve cover gaskets, C6 tranny gaskets and modulator, axle seals) completely gave out and it could hardly move out of the puddles of it's own fluids!

First thing I would do would be to pull the dipstick and give it the old "sniff test" - see if it smells more like gasoline than oil. But then, the fuel pump
was the first thing I changed on that truck.