Even though that's supposedly a Cat 1 hitch, I'd be concerned - even if a rear splitter didn't lift the front end off the ground - that the TPH couldn't lift the splitter to a sensible working height. The hydraulic pump might also give you a cycle time that would permit a nap between splits.I have a 2004 JD X585...?
I built one and used it on my Kubota B2910. But I used a 22gpm PTO pump. I loved that splitter. Lost it in a shop fire. I would be concerned that your tractor hydraulics can run a splitter fast enough. Nothing more aggravating than waiting for a splitter to cycle.
. . . With your tractor, it is so small and seemingly special purposed (lawn care) that my counsel to you would be to look into purchasing a standalone splitter.