I just chased a similar deal on a friends 70 Coronet R/T. Ported heads, small cam, stock intake and exhaust manifolds, AVS carb. I could have sworn it was a carb issue, wrong. Ran great then as it got hot it would stall, Pump it and it started right back up. I started checking voltages and found the coil voltage low. Back tracked to the ballast output and it was low. Tested the ballast input and it was low. All the readings were taken while running by back probing. By this time I ran a jumper wire from the battery to the ballast thinking the ignition switch circuit was compromised. The voltage didn't improve but the car continued to run. On my way to the next test the jumper was removed. Removing it caused the car to stall immediately. Several more times the jumper was reconnected and removed, stalled every time. The coil + voltage was still low even with the jumper. The ballast resistance was checked and found in spec at .5 ohm. I replaced the coil with a known good unit thinking the original coil winding's may be shorted causing high amp draw/low voltage. The substitute coil is still on it. Hasn't stalled since.
Doug