I LOVE your idea! I had thought of this, but couldn't quite imagine a home-buildable version, and here it is!
I seem to remember that Comet once made a mini-bike transmission with two chains.
Regarding the technical details. For better meshing, I agree go with 4 studs 8 holes. If you have 8mm studs try 9mm or 10mm lightly chamfered holes. The play will only "come into play" at the moment the kart transitions from drive to coast and back and won't be noticible from the driver's seat. I think the improved engagement will outweigh the play.
The chamfer is important. The angle should be the same on the studs and holes, with the tips of the studs rounded. Do not make too much chamfer as this can make for more difficult shifts when drive and driven speeds aren't well matched. This is analagous to the chamfer of the "drive dogs" in the synchromesh illustration, and it is this chamfer that holds the gearshift lever from moving forward into gear when you try to shift your car without the clutch.
Synchromesh might be easier than you think. Wave washers alone will heat up from friction and lose their tension. How about a wave washer pushing a disk keyed to the shaft, with a brass face or washer to contact the driven unit that the shift is approaching. Choosing the thickness and tension of the wave washer is important too. Too much tension or too soon friction application, and the clutch might be stopped and held where the studs aren't aligned with holes at all. The best solution for this is to have so many holes that their chamfered edges overlap so that only chamfer-to-chamfer contact is possible at engagement; again see the synchromesh illustration. Since it is better not to have too many holes, rounded stud ends will help the studs skate along to the next set of holes. One stud slightly longer than the rest will reduce friction here, but otoh concentrate engagement forces on that one stud.
A wet bath system is uncalled for with chains. If the gears and sliding member are riding on sealed bearings that is great, some graphite chain lube spray on the sliding member shaft when you're spraying the chains, and some sparing grease where the shifter contacts spinning members, is all the lube you'll need.
One thing that will help engagement would be to replace or recalibrate the centrifugal clutch so it engages and disengages at higher RPMs. There is a sweet spot between helping shifting and affecting overall kart performance.
Hope it helps, and thanks for sharing your interesting build!
