A bad vacuum advance will cause surging as it keeps adding and losing timing. unplug it and see if that clears it up.
It the car an automatic or a stick? What do you mean by going slow? Is it 5 mph, 10 mph, 30 mph?? Does it surge at any other speed? Does it idle well?
No the carbs. are inside and dummies on top ? Will do when weather gets cooler. It feels like 100 Deg. here.
I'm surprised nobody yet has mentioned lean surge. Are you sure it's not lean in the range you're talking about? When I built my 46, took it for its first drive. It has a used Demon Carb that my friend had on a 454. It was surging a lot at slow speeds, 20mph-ish. He had it jetted down from 70's that it came with to 62's. Put it back to 70's and it stopped surging. For surging I'd check fuel delivery and jetting first.
Loose carburetor...? Just worked on something similar to this. Engine would run rough and surge while driving, but would idle fine. I found the carb was loose, with the bolts less than finger tight. Throttle action would lift the carb off the gasket just enough to cause a vacuum leak. Vacuum gauge didn't show the problem because at idle there was no throttle action and the carb would sit flat and seal. Weird one and a first for me.
Is this set up new to you? Meaning, did it always do this, or is it a new condition? Knowing this could rule out tuning/fuel curve.
I had that issue on my 62 Chevy. At a certain throttle position, the steel throttle linkage contacted a plug wire and it eventually rubbed through an area and would miss at that speed.