Trouble diagnosing problem

I'm having a bit of a problem with my 73 Duster. 360 engine. Stock carb.

I bought it last Saturday from a really nice guy who lives about 83 miles away from me. He said he filled the tank for me but on the way home I "ran out of gas" with about 24 miles to go

I put that in quotes because I seriously don't think I actually did run out of gas now. When it happened I took off the air filter and tried to squirt gas into the carb but nothing came out. It took about 2 1/2 hours to get to a gas station and fill up my little 2ga gas can and get back to the car. I poured 2 ga in squirted a bit in the carb and drove to the gas station. I expected to put quite a bit of gas in but it only took 8 gallons before overflowing.

This got me thinking maybe it only has a 10 gallon tank. But I texted the guy and he sent me the part number for the new tank he installed from custom industries. It's a 16 gallon tank. The tank looks brand new AND I can't find a single 10ga tank manufactured for the Duster ANYWHERE. They don't appear to exist. Additionally my tank matches the measurements of the model he says he bought.

So probably not a 10ga tank and probably didn't actually run out of gas. I start thinking bent or miscalibrated sending unit, maybe the wrong unit altogether.

I took a pic of the odometer when I filled it up. I then drove home and then drove my wife around a bit before we went home she wanted me to fill it up again fearing we would run out of gas

So I go to the gas station and it only takes 4.84 gallons before it overfills. I take another pic of the odometer and a little math tells me I had driven 88 miles on 4.84 gallons of gas. Not bad.

I drove the car again for two days just to and from work plus a little detour due to traffic. Then tonight the wife and I are stopped at a red light and the car "runs out of gas" again. Dies. Cranks but wont start.

Push it across the intersection to the gas station and it only takes 5 gallons of gas before overflowing.

Head home pull into driveway put it in park and it starts chugging then dies. Again strong crank no start. I wait 30 seconds or so frustrated then try it again and it fires right up. It has a mechanical pump so my thought is maybe vapor lock. Especially since it's been over 100 degrees Fahrenheit the last few days.

What are your guys thoughts? This is the same car with a non functioning gas gauge at the moment.

Will an electric fuel pump solve the vapor lock issue if that's what it is? What else might it be?