Route your leads over the top rather than underneath.  It sounds like your plug leads are breaking down under load.  Your "getting hot" problem may be part of that.

i had the same type of problem with my car.   my car was also switched over to HEI instead of the original coil/points.  

I had ran a new wire when I had a Pertronix Ignitor module in it. I ran it directly to the fuse panel, to a tab labeled Ignition. I know the resister wire is a issue.

Thanks

Did you test the fuel pressure while driving it, or just sitting idle?
There are several things that come to mind for this problem.
1) Ignition
2) Fuel
3) Timing
The fact that you can "ease" into it, and it seems ok, kinda points to a fuel issue, to me. Could be a clogged filter, or the "sock" in the fuel tank is collapsed. Could also be a lean condition with the carb.
Have you pulled any of the plugs to see what they look like?
Many questions will follow...

Might be fuel....

4 pounds is a bit light, for a biggy-block. I'll almost guarantee it is dropping to almost nothing when you goose it down the road. You really should have around 6-8lbs.
You would need to "T" into the fuel line, after the pump, get get an accurate pressure reading while driving.

The only real way to check the sock is to remove it from the tank. You can, however, get a good flashlight (NOT a lighter, or electric drop-light), and look down into the tank from the filler. You can see the sock on the end of the pick-up tube. That is, unless there is too much poop in the tank, in which case, you've found the problem! If you can see rust, or any other kind of crap in the bottom of the tank, that stuff will clog the sock over time. You may need to drain the tank, or drive it 'till it's low on fuel to see the bottom of the tank. I can see the bottom on mine(the '74) when it is full, but I have a fairly new tank, that came with-out the funky rust option!

You might try to blow back thru the fuel line from the pump suction side, into the tank, and blow some of the poop off the sock, and see if it drives better for a while after that. If it does, then you've narrowed the possibilities.

Fuel... so it might not have enough flow...

How old are your plug wires? I had the same problem and changed my wires and that did the trick. They were breaking down under a load.

The distributer and wires are new as of last week. I changed from a Pertronics Ignitor module in my stock disributor to the new HEI setup.