True, true - chains can be both messy & noisy, yet the (marginal) friction losses of a belt drive yet w/all the same or worse tensioning issues resulting in slip (suspension travel too), I figure for this app, chains were the way to go...
Belts are a nice option for a standard bicycle four stroke conversion tho, I'm sure you're familiar with
Wizzers?
I wish ya had a coupla pics of your ol' "trike go-cart" lol, such beasts are always awesome to behold