Klett -- good post. Knoot -- good answer, mostly. Please allow me to "be more helpful:"
First, the engine:
You didn't say what engine was on your Honda HT3813 -- single or twin. I presume it's a Honda engine.
In February of 1999, I attended the Kohler Engine Level 2 Factory School, and on Thursday afternoon of the 5-day school, the class was given two Command 25hp V-twin engines to "do with whatever you'd like." Since in our shops, we only see an engine needing repairs after it's been damaged, we decided we'd run one wide open and the other without oil. For the wide-open engine, the instructor wired the governor open, set the engine stand outside (just in case), and started it up. The tachometer read 5700 RPM -- for 45 minutes! It never missed a beat, and would have run faster but the valve springs began floating, so 5700 was its maximum RPM-- well above the "recommended" 3600-3800 RPM. And the short strokes of our mower engines do help keep metal stresses within limits.
So...with Honda engines being a comparable quality to Kohler, I wouldn't hesitate to do away with the governor. Carburetor and manifold size, as well as the ignition system, will likely be the limiting factors on your RPMs.
Next, the transaxle:
Again, you didn't say what transaxle/transmission is in this mower, but I don't see a problem keeping the shaft drive and going with a Peerless 820 transaxle. The heavy-duty 820 transaxle can be mounted "vertically" with the input shaft horizontal, axles at the bottom, and cluster gears above the differential. There are also higher-speed final-drive gearsets available for the 820 that allow the axles to turn faster with no increase in input RPM. What you would need to be careful about with this setup is how the transaxale input shaft disconnects from the driveshaft for the purpose of shifting gears. And Knoot did have a good point about being able to vary pulley sizes for more ratio possibilities.
Again, I believe your "keeping the driveshaft" is doable. If I can be of further help, please let me know. The high-speed Gearset Upgrades are available on my internet store site --
ROMs-Peerless-Transaxle-Supply.ecrater.com .
I also offer new 820 transaxles.
One thing is certain -- you would have one unique racer.
Decisions, decisions...
Respectfully,
Rodney Rom
Kohler Expert Technician
Peerless Gear Master Technician
Rom's Reworks
Butler, MO