I have similar trouble, you may have seen my photos of moving 15 foot logs with my loader, which around here is mostly oak. 62-64 lb./ft3, so even small logs are over 1000 lb., and I occasionally end up bringing home single sticks weighing up to 5000 lb. Like you, the area where I do this firewood work is not flat, mostly due to a combination of my own activity and erosion.
Always keeping the bucket or log as close to the ground is important. I've had a rear tire come off the ground more than a half dozen times, but all but twice I had the loader bucket low enough to the ground that the machine stopped with one rear tire just maybe 4" off the ground. I also keep my
ballast box lifted as low as possible, without dragging, as that gives best side-stability over carrying it high on a side slope.
Also, don't be shy with ballast weight. I have something like 800# in my tires, plus 750# fixed weight in the ballast box, plus another 680# of suitcase weights I hang onto the ballast box when doing real heavy loader work. That's about 2230# of ballast beyond the weight of the machine itself, and since nine of those suitcase weights are hanging way off the back of the ballast box, their leverage is amplified well beyond their weight.
Of course be careful with too much rear ballast when driving uphill with an unloaded bucket or bucket removed, it's just as easy to go wheelie and walk a machine over backwards onto yourself, especially if it's gear drive rather than HST.