I looked at the specs for your ZTR and found it quite a bit lighter than my Deere 757 60” by about 500 lbs and have never felt mine ever try to slide, even with turf tires. So I think your thought of adding weight should help. It’s hard to compare when you didn’t give any specifics other than “hilly”. My tires are also significantly bigger & wider 26 x 12-12 which likely improves my traction. Others have had great luck with the steering wheel version Cub Cadet ZTR on “hilly” terrain so I know there is a solution. They may be more expensive models, but nothing trumps safety. Mine is an older version commercial model. You may find a commercial version may be a solution, but at a cost.
Do a search on MTF and you should find something.
Do a search on MTF and you should find something.