Here's a follow-up since I finished mowing.
I managed to do the steeper areas I had been concerned about. I put them off until I had done most of the other mowing. This helped since I gained confidence with the tractor the more I used it.
What ended up working best for me was to just drive straight up and down the steep parts. It was a lot like it had been with the ATV mowing setup I had. I used low gear, 4WD, and took it slow with the FEL fairly low. I didn't slide and only had to back off and re-align a little a couple times when I got onto a bump.
The tractor feels more unstable than the ATV when traveling sideways on an mild incline. I had mowed this way with the ATV for some of the lesser inclined areas. With the tractor I changed most of my rows to be more aligned with the hill's up/down angle even when it wasn't that steep. That worked out well too.
Apart from a rough first day when I had some fluke stalling issue (which I mentioned in another topic), the tractor worked well. It's a nice upgrade from what I'd been using before. I'm glad I got it and feel like mowing the field should be no problem in future years.