65 Barracuda daily driver

So, I've had some issues with the car not starting when it's hot and also stalling when idling and leaving a stop sign/ traffic light. At first I thought it was the ECU that is pretty close to the exhaust manifold on the slant 6. I had a couple of them laying around, so at first swapping them seemed to fix it. I'm not so sure about that anymore. I'm sure that there are some fuel boiling issues as the carburetor gets really hot. Also, I ran out of gas not too long ago and in the past that has lead to similar issues. For some reason running out of gas appears to destroy the accelerator pump it - is that a thing? Anyhow, I'm pretty sure I have to rebuild the carburetor, which sucks, because ideally I will swap slant for the 318 soon. Did anyone have similar experiences?