There is nothing wrong with building a mower for those once a year events...believe there is one in Indiana that's been running a year or two!
You need to go to a direct steering set-up, do a search for "irect steering and you will find many different examples, for your one race stocker, the simpler the better!
As for your statement on going 20mph safely.....20 mph is ALOT faster than you think it is on one of these. 20 mph on that machine, sitting as high as it is , it is going to be real difficullt to keep on 4 wheels! I think Top speed in the CP class at the USLMRA Points race in Macon was about 22mph!
Your on the right track by ditching that geared steering, that's one of the things that will hurt ya!
A couple more things you really need to do to be safe at that speed is fix the front end, and most importantly, you need axle mounted brakes. That little trans axle brake will burn up in about 10ft!
Asa for the Karts....they are great...for parts