So no pictures but my update...
The 715 belt that came with has been working pretty well. Or, at least not getting torn apart quickly.
Swapped in the 673 that GPS sent just for the heck of it, and I'm not sure I feel any difference. After a handful of hours, it seems to be about the same performance as the others.
The kart has settled down on idle with the shifter in drive. After starting I still have to have full choke when going into forward before apply throttle and pushing the choke in to go forward, or it'll stall. I tach'ed the engine and was at 1300-1350. Without looking at a spec, that felt fine.
After the engine and belt have been run for a few minutes, it hangs out at idle without moving much better.
Overall, probably won't do anything else on the belt front. I have a couple comet belts as spares (past the return window). If they don't work, I'll get more 673's or maybe try 669s again.
Both kids have been driving the kart and loving it. Get home from work, and it's almost a routine to do 10-20 min driving the go kart around the yard. The 4 year old (almost 5) can steer and accelerate. The 3 year old stretches to apply gas and gets help steering.
Overall, it actually exceeded my goals (yard kart I could fit in and the kids could drive it be close to driving by next year).
Will get the phone to do some GPS speed timing just to see what we're going in the near future.
So.. if I wanted to upgrade the engine exhaust/intake/anything else, where do I start? The evening is described as
Engine type 4-stroke, single cylinder, air cooled, Horizontal OHV Engine
Displacement 208cc, 7.5HP
Max HP 7.5hp/3600rpm
Max torque 8 lb ft/2800rpm