I also have a 3038E JD tractor.
The rear wheel tread is not adjustable like larger tractors so the wheels can not be set out wider. That is one of the best things to do to make a tractor more stable on slopes, widen the tread width to widest available. Can't do it on this tractor.
One thing that will help a lot for not only stability on side hills, but also for loader use is to put ballast on and in the rear tires. I have two sets of cast wheel weights and also had the rear wheels filled 75% with windshield washer fluid. Most ag tire dealers can do this. You can get more weight with a clacium chloride solution but if you get any leaks it rusts the rims terrible. The windshield washer fluid (available in 55 gallon bulk barrels) will not freeze and will also not rust the rims.
Adding adequate ballast to the rear wheels lowers the center of gravity.
If you have a loader on and are mowing on a side hill, never raise the loader up in the air over a few inches. Keep the bucket as close to the ground without it being a problem hitting. This also will lower the center of gravity compared to a loader lifted higher.
A belly mower will be more stable than a rear mower. I use both a 5' rear rotary mower and also a 72" rear finish mower. Both will try to pull the back of the tractor down hill where as a center mounted mower will be balanced between the front and rear wheels.
I do not use my 3038 on the back of my dam generally, though it is a low enough slope I can (barely). I either use a 15' flex wing mower behind a much larger tractor or if I want it finished looking for a party or get together or something I use my 72" Bad Boy Outlaw XP zero turn mower. It has a significantly lower center of gravity and a significantly wider wheel tread than my 3038. Plus it does a significantly better job than the tractor finish mower.
Mowing a slope up and down you can mow a significantly steeper slope as mentioned. But you have to have a suitable safe turn around area top and bottom (turning up hill on a slope that is steep is the last thing you want to do). About half of my dam backside is bordered by a small creek with a drop off.
Hope some of that info helps.
Last edited by snrub; 02/02/16 12:40 PM.