Modern fuel is designed for an EFI system and not an open bowl vent that a carburetor uses. In some applications the fuel vaporizes from the heat and either slightly vapor locks the carburetor or mildly floods the engine. You may want to try opening the hood as soon as the engine is shut off to lower the temperature of the fuel in the carburetor and also, holding the throttle slightly open with the accelerator as you crank the engine to restart it. This will allow a little more air to get in.
If the float and bowl vent are set properly and the engine does not use a heat riser that is stuck on, then it should start well and not be an issue. Most carburetors that are sensitive to modern gas to such an extent that they are hard to restart have a problem with one or more of the three areas I listed.