You have some cable adjustment up on the handles under the air filter, loosen the 2 x nuts and the bracket slides up or down a bit.
All mine are mounted on the inside, so you could flip yours around to match the one in my image.
I would jack up the back wheels and watch what the belt is doing when you push the SP lever.
Your locking wheels in reverse is a worry, you should be able to pull the mower back (it shouldn't lock) because when you are mowing you need to be able to get out of a corner.
Are the wheel drive cogs reversible? I cant remember, I think its the Honda SP that has a Left and Right cog that cant be swapped.