I have the same issue with a '71 /6 Dart I just got. I think you are describing the same thing I noticed. I've not tried to restart the car as at the moment I'm just trying to tune and do the mechanical on it before we drive it regularly, but I did notice what looked like the petrol perculating in the filter until the filter was empty.
When I noticed it was after running the car to set timing etc. and the engine is to operating temp. if I shut the car off and then come back a moment or two later I can look at the clear fuel filter and see it bubble as if the fuel is draining back somewhere or something. The bubbles are not a rolling boil like a pan of water or the like. Just sort of a bubble, a moment or two passes and then another bubble.
The fuel line comes up the front of the engine as a metal line. Just before the carb the line stops and a clear fuel filter is connected inline using rubber hose and clamps. Then the metal line continues out of the other end making a curve (have a Holley 1920? type carb) to connect up to the carb inlet.
As I said, it will keep doing this until the filter looks empty of petrol.
Sound the same as you? If so then that is two of us looking for the answer of what to do. My thoughts thus far is some sort of heat issue, fuel pump issue allowing drain back (guess I need to double check there is no petrol in the fresh oil change I did), I've semi discounted the carb as I just put a kit in it, but then who knows????
I certainly don't want to have an issue of us driving the car and then getting stranded with it not wanting to restart.
Cheers
