Yeah, running a mower on the 3ph will change the balance. Suitcase weights on the front may be better than the loader though - the loader sits quite high compared to the weights. Ideally you want your weight axle height or lower.Taking off the loader might be the ticket. I have to try that! Is that a "duh" moment for me? Thank you for suggesting that. I'm mowing with a 6 foot (180 cm) finish mower or a 4 foot (120 cm) heavy duty bush hog.
My dealer recommended leaving it on for forward ballast. So I never thought to try without. Easy enough experiment. I've never taken it off. So that would be a good learning point for me regardless of mowing side hills.
Speed? I creep when things get sketchy. Like ready to jump slow. I have one trail I can mow, but I am sideways crab walking. Pucker factor galore.
With the loader off, you should find lots more traction in 2wd on the flat. And also a lot less pitching - I find loader + 3ph implement equals lots of pitching back and forth over bumps. But you may find your front wheels pretty light, so turning will now be a bit more of an issue. I can't see that you'd tip over backwards (the mower would just hit the ground), but on side slopes now all your traction is coming from the rear. Which might be fine, or might be a real problem if you need to turn quickly for some reason.
Anyway, worth a try. Nothing to lose from it.