Put an oil pressure switch in the ground side of the relay's coil circuit. This will keep the fans from coming on till the engine has oil pressure and you're less like to forget to turn it on as it's automatic.
Again, I reiterate, the contacts inside the starter are likely the culprit. I linked to a replacement set above. Cheaper than a new starter.
They say there are no such thing as a stupid question. They say there is always the exception that proves the rule. Don't be the exception.
