Surging (revs low and high over and over again) is usually an indication of a fuel issue like fuel starvation.
Could be clogged jets, clogged fuel tank vent, dirty fuel, water in your fuel...
Needless to say, fuel and fueling up the bike, for instance, is an exercise in cleanliness. Gotta have clean, good quality fuel going into a clean jug (at the gas station) and your bike's fuel tank should be clean. Some people pour their fuel through a filter before it goes into the vehicle fuel tank.
Do you have a fuel filter between the tank and the engine? Check it for clogging.
But nevermind all that for a minute. THE truly shocking thing here is--you've really got no business trying to keep up with a "Kawasaki 1000"!
That's just nuts. You and your brother and friends should be riding either all minibikes or all street (or dirt) motorcycles.
You
can keep up with a Kawi 1000 with a modded industrial engine (that's what the Tillotson is) for a while, maybe, but what the Tillotson is doing at its very limits (redlining it), the Kawasaki is doing with ease. It's apples and oranges.
You should try forming a minibike group and doing something like this:
Looks like fun.