Not sure why a higher octane fuel should be making the car harder to start. It should be the reverse. Higher octane fuels are generally better for an engine. Maybe the 98 fuel tank from wherever you buy your fuel from is contaminated with moisture?
Maybe try 98 fuel from another place and see if after 2 or 3 tanks you have the same issue.
Problem sounds like a battery getting weak or bad battery clamps, earths/contacts or tired starter draining too much current. If the car isn't firing up properly, it could also be a sad fuel pump, dirty injectors or a blocked fuel filter causing the miss until the fuel pressure comes up.

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