I understand Briggs & Stratton disapprove of running the engine without more of a flywheel than is provided by the magneto & fan assembly that is commonly called the flywheel. I think you'll have a bigger problem than that in trying to use a vertical crankshaft engine in a go-cart, though. You can't run the mower engine with its crankshaft horizontal - it wouldn't lubricate, and of course you'd have to redesign the fuel tank and carburetor.
You can remove the blade-plate mounting boss, but I wouldn't do it just to remove the broken bolt. I'd drain the oil, then set up the motor and baseplate upside down under the drill press so I could drill down the center of the broken bolt and remove it with an ezy-out. Before going to that trouble, though, I'd try just using a very small chisel or centerpunch to see if I could unscrew the broken bolt. Bolts that weren't bottomed in a thread usually require very little torque to unscrew them, unless they have rusted in.
