There are clubs for the real MOW putt-putt speeders. I always wanted to do that or velocipede around for a bit.
I used to put weedwacker motors as friction drive cruising motors on my old bicycles; Solex style. About 25-30mph & about 70mpg.
...and a guy I rent a room to has 3-70mph mini-bikes (a few original "slow" ones) and a half dozen hopped up motors kicking around 3hp B&S to 6hp-Honda's with headwork, race clutch, race carbs/exhuast, etc
....I'll be needing a railcart with wheelie bars too as my choice of air cooled motors would be a 1200 to 1500cc "Beetle-ee" engine from VW