Maybe I am misunderstanding something, are you not going to mow while backing up the hill?
I have mowed slopes like this with a non synchro gear model, synchro shuttle shift, hydraulic shuttle shift and HST. It can be done with all, but it is harder when you have to shift gears. Just keep it in 4WD and brakes on when you stop to change directions. You might want to practice on something not so steep. There is nothing wrong with waiting for another time or just not doing it.
My original plan was to only mow forward...but that went out the window quickly. I used 4wd and 1st gear. I did the base of the hill and what I felt comfortable turning on in a typical "zamboni" method. Then I backed up the hill mowing and was planning on stopping when I got scared. I wound up not getting scared too badly and just went all the way up. The machine didn't high center. I moved over and made a pass down. Repeated this about 3 times and I was done with what I think the tractor could do.
The full overhead protection system on my L39 really makes me feel safe. I strapped myself in and covered the brakes and clutch or shuttle lever at all times. Overall it was a puckering, but good experience. I will mow it this way again in the future as necessary.
I will try to snap a few pics tomorrow since it got dark on me. I hope the pics do it justice as this hill is no joke.
ac