Well, there are a couple of areas that my current tractor (late 90's cub with manual) will speed right up and if I'm in a high enough gear will get hauling pretty good. I usually mow that area sideways. There are other areas that are downhill for long distances but not very steep. I'll have to give it a try and if needed at least theres a 'fix' for it.
Prior to "giving it a try", please go to the Tech section/Operator's Manuals and READ CAREFULLY the procedure for controlling the tractor on steep grades using the travel lever. This is an 800 pound tractor. That's enough weight to do some serious harm to your body parts if it ends up on top of you.
Secondly. that "brake" is not really a brake in the true sense of the word. It's a parking brake primarily so don't rely on it to stop the tractor. And if you do step on it, there is a spring that is designed to pull the travel lever into neutral and that's NOT where you want the travel lever to be.
Lastly, any braking mechanism is only as good as the amount of traction the tires can find. OEM turf tires are not known as high traction rubber. Steep hills often require the use of tire chains, wheel weight, tire loading and even Ag-style rubber.
An out of control tractor is dangerous. It's only funny if you survive the ride. Some new owners that have experienced such a ride have sold their tractor right after.