Quick Fuel Tuning

It sounds like maybe you're lean on the primaries. I'd first check if your secondaries were opening too early (spring pressure too light maybe). You can put a zip-tie or some grease on the secondary actuator to see if it has opened (the zip-tie will be pushed down or the grease wiped off if they've opened). This is not likely but it doesn't hurt to check. You could also have a problem with your timing, I'll assume the distributor and vacuum advance are in good shape and timing has been set properly.

As you mention it does it while you ease into the throttle, it's not likely a problem with the power valve. I'd suspect the primary jets being lean but as you mention it could also be rich (check a spark plug to see which, and it the car smells strongly of fuel when it hesitates). It's a bit of a guessing game with a carb, though installing a wideband O2 sensor can also help a great deal to figure out what's happening. I have one in my carbureted turbo II.

So keeping with the guessing game, you probably should get some different behavior if you mash on it vs. smooth acceleration. When you mash on it, the accelerator pump and your power valve should be helping to enrich things. I'd suggest making sure the float level is good, it may be too low. I don't know much about Quick Fuel carbs, but I believe the level's supposed to be half way up the sight window. You said you adjusted to half-way, not sure if that's what you meant.

does it run a accel pump? might need to bump up a size on those also