You'd play golf and quietly run everything smoothly.
Congratulations, you got the guy who literally invented the interstate highway system and still found time to play golf twice a week. You and Ike would get along just fine, probably over a quiet dinner where neither of you feels the need to be the loudest person in the room.
Eisenhower was the rare combination of supremely competent and genuinely unassuming, a man who led the Allied forces in World War II and then somehow managed to make the presidency look calm. He warned the country about the military-industrial complex on his way out the door, which is the historical equivalent of dropping the mic. You clearly have a thing for people who are understated but absolutely right about everything.
Your match with Ike suggests you value stability, practicality, and getting things done without a lot of unnecessary drama. You probably don't need constant validation, you just want solid results and maybe a decent putting green. Ike respected competence, kept his cool under pressure, and had zero patience for pointless spectacle. Basically, he was the adult in the room before that became a cliche. No wonder you two would hit it off.