World Formula is pretty popular here in the PNW! They even road race them at tracks like the Portland International Raceway.
One possibility for avoiding the vast cost and unreliability of “built” 4-stroke engines is to use something that makes enough power stock and completely worn out that nobody will want more. We’d have to change the design of the karts to accommodate it, and the cost of the dry-sump system, cooling, and electronics needed to run it would be very high, but it’s likely that the powerful parallel-twin engine from a Yamaha MT-07 or Honda Hornet 750 would have a long lifespan with all plain bearings, electronically limited engine speed, and violent wheelspin available on every corner exit!
Note - this is not the MRC/Factory company line; I work for General Atomics now.
Might be easier if your lines are just your own 
That’s a big slug to bolt to a kart chassis 
Not sure if the juice would be worth the squeeze as a class, but it would sure be fun to try and drive…. If you could convince underwriters to let 750 twins run.
In related but not really related , a downsized version of the 700 rotary from the Crighton would be epic as a shifter. Probably epic cost too.
It is a real shame a Wankel has not seen adoption in karting. They really do lend themselves to the application. The XR50 would have been bombastic as a shifter.
On a sprint track you’d finally have adequate power - you would still be managing traction halfway down the main straight. Keeping the tires from overheating would separate good and bad drivers quickly.
At minimum, the driver would have to be shifted further left to balance out a 100 lb monster and get them away from the viciously hot exhaust pipe and catalytic converter, and both sidepods would get moved out to mount the engine and radiator. It’s likely that the tank and pedals would have to move as well, and you’d probably want to move to a wider rail spacing on the engine rails to be able to keep both crankpins over the frame. The large chain and sprockets might need something better than a flimsy little key connecting it to a mild steel axle. Fuel tanks would have to have the fittings to mount the in-tank 40 psi pump.
You could encapsulate pump in a separate tank as well if needed. Feeding that tank with a pulse driven one pump. I’ve seen some EFI snowblowers done this way. When I’ve been mulling my EFI system I’m not thrilled about running a pressurized line from the tank. But I could be overthinking it.
I’m curious to see how the EFI CRF250’s were setup when they were a thing.
Meanwhile, back to Wankel:
Bryan how far did you get with the project?
I should add…… On my end, last year I grabbed three pit bike engines to test out. Goal being a four stroke shifter that’s comparable in performance to the 80 two strokes that were so popular.
Zongshen ZS190/212 (5 speed, 2v OHC)
Daytona 190 4v (5 Speed, 4v OHC, long stroke version)
Yx platform: ThumperX (4 speed, 2v, 208cc)
At his point I’m focusing on the Thumper X as a base after testing the Zongshen and Daytona (also made by Zongshen).
With the yx base you can have more parity across batches (Via CNC head work) and increased longevity of parts compared to the Zongshen stuff. One issue I ran into with the Zongshen gear is that it doesn’t quite have enough material near the valves to bring them all in line consistently. Tougher transmission with the 4 speed is a bonus, and to be honest most of us only use 3-4 gears out of six in a shifter anyway.
I’m working on some revisions for cooling (needs more), fuel (EFI or at least simplified fuel setup), starting setup (stock is terribly underpowered) and ignition (Ditch the garbage “China” CDI and move to analogic PVL setup)