Sounds like your symptoms are different, but here's my story.
Q-jet, rebuilt, everything good as can be inside and out.
Driving along the freeway at 60MPH, try to accelerate up a hill, vehicle would start to sputter and miss. This was pretty much totally random as to how often it occurred, but always seemed to occur when I needed more gas.
Last time it happened, was climbing a very steep hill. Started sputtering, let off gas, which usually "fixed" the problem. Not this time. Ended up in low with the 465, trying to climb this two lane road up a pass, and it finally stalled.
Got it backed off the road, popped the air cleaner, hit the throttle, and no pump shot from the accelerator pump. Carb was empty. Got it pointed downhill, coasted about 2 miles in gear, when it finally started.
I *suspect* that the float was sticking for some reason, (maybe rubbing on a distorted float bowl wall, or "loose" float tolerances) although on disassembly, there was nothing visibly wrong.
So fuel problems CAN manifest themselves oddly, but problems like mine are definitely not the norm.
Definitely I'd lean more towards the ignition system, new doesn't=good anymore.