I would strongly recommend against using a typical 3 point mount finish mower behind a 100 HP utility tractor on ag tires on yards that average roughly 3 acres or so, for many reasons. I used to mow a yard with a much smaller tractor with a 6' 3 point mounted mower so I speak from experience.
- A 3 point mower is not very maneuverable behind a 30ish HP compact, let alone a 100 HP utility tractor. 3 acres or so is not very large, particularly if there are any obstructions to avoid. You will spend a lot of time turning around and avoiding objects.
- You will rut up the yards terribly unless it's bone-dry so the soil is rock-hard. People here complain about a compact weighing only twice what a good zero turn weighs and riding on much less aggressive industrial tires rutting up their yards. You are about an order of magnitude worse than that with a full-sized utility tractor on ag tires that weighs 6-8 times as much as a zero turn does.
- You will actually mow at a noticeably slower speed with most 3 point finish mowers than you will a decent zero turn. In my experience 3 point mower decks don't discharge nearly as well as a good zero turn's deck does, so you will just plug up if you go very fast. Having a bunch of power will just result in burning up the belts when you plug up the mower, you will not be able to mow any faster.
- A 100 HP utility tractor will ride more smoothly over bumps and divots than a zero turn at first as it has larger tires that roll over them and the extra weight smashes the bumps and cuts ruts. Once you rut things up and later the ruts dry up and harden, different story.
If you wanted to use the tractor, I would get high flotation turf tires for it, take the loader off it you have one, and pull a big flex-deck mower. That way you won't rut things up so badly and and at least would be cutting a wide swath for the lack of maneuverability you'd have to deal with. However, it would be cheaper and quicker just to get a very good zero turn. It sounds like that is out of the budget, so I would personally fix up your current zero-turn or get a better higher-end used one.