If you use a tire with a DOT speed rating the tire has been tested at far above rated loads for a long period of time.
We should assume that racing tires have been tested in the same fashion. Even if the tire is branded "racing", all that means is that it isn't DOT rated. What is the maximum speed for that tire? You would have to contact the manufacturer. I have yet to see a speed rating for most racing tires. Despite the racing label, you have to look at the top speed the tire is likely to see in that form of racing.
Goodyear recommends a maximum speed of 300 mph for the Eagle Land Speed tires, but no ratings for the Top Fuel tire.
The killer for tires at high speed is centrifugal force tearing the tire apart. Shaving is a tried and true method to reduce the amount of rubber and centrifugal force on the tire. Smaller diameter is better. Even though the kart tire will be spinning 7,000 rpm at 200 mph it's less likely to come apart.
In 1980 Australian Rosco McGlashan built and drove a hydrogen peroxide rocket kart that surpassed 253 mph! Rosco has gone 315 mph in a jet dragster and 643 mph in the Aussie Invader 2 rocket car.