The Owner's Guide for your model has a fair amount of information that should help you get organized with this machine. You can download it here:
http://manuals.mtdproducts.com/mtd/...l_num=132-680G670&filename=770-7851g.pdf(You will need Acrobat Reader or Acrobat Pro to download the file.)
See Fig 13 on page 10. While it is not clear, the speed control appears to act by moving an idler on the transmission drive belt. Most likely one of the pulleys is spring loaded, so its effective diameter is decreased when the belt tension increases. The transmission itself only has forward and reverse gears. This is why you have to declutch and stop all movement of the mower when shifting between forward and reverse, but not when shifting speed.
I do not think your grassy slope is as steep as 30 degrees. The steepest hill a well-designed 2 wheel drive car can start on is 30%, which is not 30 degrees but 17 degrees. My driveway is 15 degrees, and the concrete has rough grooves across it to make it possible to drive up it when it is wet. The steepest slope your mower's engine can operate on safely is 15 degrees, because of lubrication issues. Normally a mower like yours would be doing quite well to operate on a 30% slope, and it would be risky to drive it across such a slope. Of course if the grass were wet the mower would slide down such a slope, whether it pointed upward, downward, or crossways on it.
If your mower will operate up a 30% slope in second speed, that would seem to me to be very good performance.
