Greg;Check to see if you are getting spark when it doesn't start. The old method of disconnecting a spark plug and laying it against a part of the engine block should work. If there is no spark then trouble shoot the ignition circuit. I had a Mopar years ago that exhibited the same problem and found that there was a ballast resistor in the ignition circuit which opened up under some conditions and caused an intermittent no start situation. If you do have spark, then trouble shoot the fuel system. Make sure gasoline is getting to the carburetor. It could be something as simple as vapor lock. If that is the case, insulating the fuel line from pump to carburetor should help. Also make sure the line is not too close to the exhaust manifold.
I assume your car still has a Carter AFB (aluminum four barrel carburetor). Those were not known to have many problems. The later cars ('69 & up?) used Carter Thermoquads and those often develop cracks in the phenolic body part of the carburetor. That causes fuel to leak out of the bowl of the carburetor until enough cranking pushes fuel back in to fill the bowl again. It sounds like the gasket set you installed would have eliminated the possibility of the fuel being cooked out of the carburetor since there is no longer any exhaust gas going underneath the carburetor.
Joe
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