Jed, We are having the same problems with my boss's '41 Ferd. These old flatties appear to be designed to induce "vapor lock" and the "easy" solution most often used is to add a booster elec pump.
A lot is being asked of the ford diafram pump. It sits high at the back of the engine level with the carby and it has to pull fuel a long distance from low at the back of the car and the fuel line is heated quite a bit as it goes up over the engine.
By contrast, our old stovebolts gravity feed from a tank closer to the engine, high in the cab, to a pump low on the block, opposite the side where the main engine heat occurs.
It doesn't take much to to get to the point where the mech pump is trying to suck flmes. Sometime's it could be as simple as winter-formulated gas (vaporises easier) used during a warm spell.
There is lot's of info on this in the early v8 forum over at fordbarn.com including the argument that there ani't no such thing as vapor lock.