this might sound silly to you but it happened to my father in law . he bought a new battery for his OLDS with a 455 cid engine ,the car would start when leaving home ,if they went shopping there was no trouble ,but a quick stop the car would not start . upon my checking it out found battery had a low cranking 550 amp .slipped in a used 800 cca battery and never had a problem again .

An engine needs 3 things 1. compression (100# + every hole minimum) 2. spark 3. fuel. I'm guessing this vehicle is original, so it probably has a 2bbl carburetor and a points ignition. 1st. Take off the air cleaner when cold, warm up engine real good, shut it off and look at the carburetor air horn and see if there is a white vapor coming up out of it. If there is, then the float level is too high, and unburned fuel is going down the intake manifold causing it to flood the motor and start hard, especially with a points style distributor. The 2GC carburetors can be touchy on the float levels. If it does have points, check the dwell (30 degrees) 2nd. If the distributor has been swapped out to the H.E.I. style, then the ignition module inside the distributor probably needs to be replaced. (warm up engine, shut off, check for spark at spark plug end of plug wires) I hope this will help.