Carby options for off road ..

Maybe find a dirt bike carburator, those ought to have some kind of mechanism that prevents bumps and jumps from bogging them down.
19 mm Honda Style ATV & Dirt Bike Carburetor with Right Side Choke|Monster Scooter Parts
It says for a 4 stroke and I'm not sure what size intake our engines have but just an idea I suppose

You will need a diaphragm carb. Something like a walbro. They have no float bowl, and pump the gas in. Another plus, they don't need the fuel tank to be above the carb.

mikuni makes a lot of good carbs. Their round slide carbs (VM series) were the standard on most Japaneses off road and enduro bikes from 1970 to the late eighties and they were replaced by the square slide series that are standard today. Neither one is a diaphragm type but either one can handle whoops and jumps just fine as demonstrated by every x games since 1994. The one you are looking at looks kind of like like a vm knock off but you can get the real deal for a little more on ebay.

I ride off-road all the time and don't have that problem.

The only time I have seen that problem is when the float level is too low causing your motor to starve for fuel. Or you have a poor wire connection that comes in to play with the bumps.

The carb needs a shroud or well in the float bowl to control fuel splashing. Don't know how you would go about building one but thats the issue. Motorcycle carbs are designed to keep the main jet covered even in rough use. Look at a dirt bike carb and try to copy the jet shroud or well in JBweld maybe?