I built a racing mower a few years ago.
To go fast all it takes is about 15 minutes and a smaller pulley with appropriate shaft diameter on the transaxle.
You can get them off the shelf at Tractor Supply Store.
I couldn't say not to do it enough though.
It will be fun for about 10 minutes,then you will realize that not being able to stop at such speeds scares the hell out of you-and I was on flat pavement.
Mower's have NO brakes,the small disc on them is to slow and stop it for shift/gear change and that's it-they aren't made to stop a mower at even top speed stock.
After about 5ft you will have zero control,because the front end is too loose.
Even brand new,they are loose because they are designed for low speed.
One thing that is cool and horrible at the same time is you will almost instantly be near top speed when you take off,there is almost no lag between stopped and ludicrous speed.
IF I were to do it again,I would do the brakes FIRST-Then the suspension/steering THEN start dropping pully size's.
You don't need to alter the governor at all,hp isn't what is making it slow. It's a function of gearing,which is easily overcome with a pully swap and smaller tires.
By the time you NEED more hp,or raise RPM for higher top speed then you'll understand plenty about racing mowers.
For now,leave it alone and fix the gearing issue with the pulley's.
It only took an 8hp tecumseh about 5m to make me realize power isn't the issue,it's keeping it to the ground.
I couldn't imagine a pulley swap on my 26hp mower,it has left black marks on my concrete just taking off in 6th!
And that was factory stock and 24hp before motor swap.