You guys know more than I about this stuff but here is my story that might help. If not, I tried. Years ago I had a 51 Ford with exactly the same issue. I checked everything and could not find a problem and I checked over and over again for months. Then one day in the warm weather I was cranking it with the hood up and looking under the hood from the drivers seat as it was cranking I saw what looked like smoke or steam coming off the engine as it cranked. Then as I stood outside and jumped the solenoid to crank it I saw smoke coming from the carburetor linkage where it attached to the carb.
Long story short, a previous owner had disconnected the ground strap that ran from the fire wall to the intake manifold bolt. When I connected that back up, hard starting when hot went away. The only thing grounding the engine and the starter was the carburetor linkage attached to the firewall which would get hot at the connection to the carb (highest resistance) and then burn off the gas from pumping and cranking at the same time. Now I always make sure the engine has a good ground not just the battery.
Long story short, a previous owner had disconnected the ground strap that ran from the fire wall to the intake manifold bolt. When I connected that back up, hard starting when hot went away. The only thing grounding the engine and the starter was the carburetor linkage attached to the firewall which would get hot at the connection to the carb (highest resistance) and then burn off the gas from pumping and cranking at the same time. Now I always make sure the engine has a good ground not just the battery.