it would not be that hard to double that speed.
Had a Wizard riding mower many moons ago, was given to me (freebie) at work. Pretty trashed but it did kinda run. Carb had something wrong with it. I was trying to figure it out, it ran out of fuel and I grabbed the can and refilled it. Started it back up, ran perfect. What? Dad filled the gas can with Methanol, which we used in the race cars. Well, it ran, so why not. Never touched the carb to figure out what was wrong with it.
later on I changed the pulleys. They come with a 3" pulley on front (roughly 3" I didn't measure) and about a 9" pulley on the back. Tractor went about 5 mph in 4th gear (4 speed) at 3200 RPM. Well I changed it up and put a 7" pulley on front and 3 on back, and in the process had to re-route and re-plan the entire belt drive,, add guides and whatnot, but it worked excellent. 1st gear was about 6.5mph. 2nd, 3rd I don't remember. 4th was about 30 mph. I had to heat and bend the front axle so it had some caster, without caster it was uncontrollable above about 12mph. With caster, it drove excellent at 30+. Also put a "tractor style" throttle pedal on the RH floorboard. The engine would run 3600 RPM on the governor, but the pedal would increase that to about 5200 RPM, so at 30mph on the governor, mash the pedal and it would kick it up to about 38 or so, just didn't have enough power to go much faster (12.5hp briggs dump valve motor).
so yes changing pulleys makes a HUGE difference. Not on HST though, they are designed to run a certain RPM and not much more. Gotta use a gear drive, and you WILL probably have to fabricate a whole new belt drive system. Dont' forget tire size will play into as well. Bigger tires=more circumference=more speed (so long as the engine will make enough power to overcome the additional drag).