Having trouble diagnosing hesitation/stumbling

I've got a 74 Duster with a 2bbl 318 that I've been driving for the last 3 years, it's always ran good. It has a remanufactured Carter BBD on it which I bought about 4 years ago, it also has a new electronic ignition retrofit kit from MP on it (someone put points on it) which I also installed about 4 years ago. The car has at least 90k miles on it and I'm almost certain the engine has never been rebuilt or opened up. I've put at least 15k miles on the car since I've had it.
Anyways, I recently did a wiring overhaul and fixed any faults with the factory harness, which made it run way better until the battery died a few days after (the splice to the voltage regulator was bad). It backfired when jump starting it, and that was when the problem started. It began hesitating and/or stumbling on acceleration, however it idles fine and runs great under WOT. I have a feeling it is a vacuum leak; the problem is definitely air/fuel mixture or timing.
I rebuilt the carburetor and fixed a vacuum leak at the base gasket without any improvement. I changed the spark plugs, checked the wires, and checked the timing. I advanced the timing 2 degrees from where it's been set at for the last 3 years to 24 degrees at idle (I run no vacuum advance, it doesn't need it), and that made it run a little bit better. I advanced the timing another 2 degrees to 26 degrees and it ran just as bad as it did at 22 degrees, so I set it back at 24.
The issue still persists. It hesitates as though it is too lean, and the hesitation doesn't go away until wide open throttle. Could it be the timing chain? I know for a fact that the timing chain in the car is very worn and has a lot of slack in it, the timing mark jumps around a decent amount. When I rev the engine in park the timing mark shows that it retards before the mechanical advance kicks in, ( the mark moves down and then up). The problem is not present when the engine is not under load, such as in neutral or park. Or is it more likely to be a vacuum leak?

So far I have:
Rebuilt and cleaned the carburetor and set it to factory specs (fixing vacuum leaks at base gasket)
Changed the spark plugs
Checked the timing (advancing it from 22 to 24 made it run better)
Checked the spark plug wires
Changed all the vacuum plugs
Checked the coil

Note: It idles very well, and runs great under wide open throttle. The only issue is the hesitation under acceleration. It's acting like it is too lean, not like it has a miss. So the problem cannot be at any single cylinder, or two. The hesitation only occurs under load.