Hei conversion Intermittent start?

If you are running a Mopar alternator, it's grounded through the frame of the alternator, IE the mount and tensioner, to the engine block.

But IF the battery is "up," and IF the HEI / other ignition is getting full battery voltage, it should run for hours without a working alternator.

Below 10V when cranking is too low, and is likely at least part of the problem.