Well, the problem is that even given no 22nd Amendment, there was a strong tradition that Presidents do not run for a third term. FDR was the only one to ever break it. You must find a way to get rid of this tradition before it begins. Washington could have won as many terms as he wanted. So maybe if he keeps running until he dies, then other Presidents will follow his lead.
Another possibility is to butterfly away Benjamin Harrison. If Cleveland won two consecutive terms, he may have come back for a third, since that matched up with his second term anyway. I know he stepped away after term two, but he got cancer during his second term, and that health scare may have factored into his decision.