Though this all started after working on the head, don't forget to check the ignition.  Be sure to make a quick inspection of the points to insure that they are opening.  When the points gap is near its limit, you can have a car that will start and run for a while when cold but be almost impossible to restart when hot.  It's a quick thing to check and once you have excluded it you can move on to fuel and vacuum leaks.

Ok I'll check all the gaskets. Would that explain why it will run fine at first but not refire with or without choke though? It seems strange to me that it will run fine at first, but I'm willing to accept it if it fixes the issue.

Sounds like a vacuum leak. Runs rich with the choke but not enough fuel with the choke off. Check manifold & carb gaskets.

Gas and Spark AT plugs and coil to the Head

I replaced the head gasket this weekend. Everything went back together ok. The engine started fine and ran for a minute or two until I pushed in the choke and it died a few seconds later. I then couldn't get it refired, with or without the choke. I tired it with the choke the next day and it fired on the first try. Same thing. Push in the choke and it died and won't refire. It just turns over and sounds like it isn't getting any fuel. I believe the carb is an HS4. I took off the dashpot & piston/needle and cleaned it but still nothing. Carbs are not my area of expertise so I'm not sure how to solve this problem. The frustrating part is that the engine would easily start up with or without the choke before I replaced the head gasket. 

Has anyone ran into this issue or have any ideas?