Does sound like gas delivery. You may have to do a new fuel pump or carb rebuild but vacuum exam first. It is sometimes faster and easier to install a new fuel pump than test it, unless you are rural. I wouldn't mess with the HEI yet. If it runs with foot in it a little, it's got spark. Advance problems show up at higher RPM's and it won't die at idle due to bad advance.
Set the idle up on carb linkage so as to keep it running by itself so as to examine, play with it and do vacuum testing.

Right is right, even if everyone is against it, and wrong is wrong, even if everyone is for it. - William Penn