A rotary cutter for the first cut. You can usually borrow or rent.
Once the first cut is done though, the question is what you'd use ongoing. That (to me) comes down to how often you want to mow, and what you want it to look like.
If you are mowing once a year and it's heavy terrain that will grow shrubby trees in that time, probably a rotary cutter. They tend to cut narrower than the other options I list, but they are heavier duty and will take a lot of abuse. Rotary cutters in this size are usually single spindle, so they're roughly square. That means they'll stick out 5 foot or 6 foot behind your 3ph. Remember lift capacity is usually rated 500mm behind the pins, you've got a lot of weight sticking way out the back. It pushes your tractor around (makes it pitch over bumps), and you may need to ballast the front or mow with your loader on - which then creates even more of a pitching motion.
If you are mowing say 4 times a year to keep it down/tidy, and maybe running some animals as well, then I'd recommend a flail. This is a halfway point between a rotary cutter and a finish mower. It'll mulch any small bushes you mow, and mulch thick grass. They are more rectangular, they don't stick out as far. This usually means your tractor will lift a size larger - if you were looking at a 72 inch (6 foot) rotary cutter, you can probably run a 7 foot flail. I've got a 2m (roughly 7ft) flail behind my MX5200. They don't make your tractor pitch quite as much, and you can mow with the loader off without needing ballast. They also tend to give a tidier finish. Having said that, they usually have a roller on the rear, and that tends to bang and crash over the ground a bit - so if your ground is really rough, perhaps not ideal.
If you're mowing once a month or more, you're starting to get towards lawn, and you probably are starting to worry about how long this is actually taking. A rear finish mower, and particularly a batwing, will give you a lot of width, and let you mow more in a given time and/or again let you run the ground speed a bit slower. If you have long straight runs (so a big flat open area you're mowing without trees etc), then a big batwing will be faster than most anything else.
Last option, if you're really serious. I've always wanted one of these:
NZ Mowers, based in Kawakawa in Northland's Bay of Islands, has been specialising in the manufacture of reel lawn mowers for over 40 years.
www.nzmowers.co.nz
35hp needed for a 5 metre mowing width - that's about 15 feet? And the finish will be like a golf course or a playing field. In theory if you put the time into levelling and cutting well a couple times with a borrowed/rented rotary cutter, you could move to one of these, do the whole 15 acres in 2 hours. Then you could cut twice a month easily, maybe even more.
(OK, I probably shouldn't project my dreams onto other people)
The other thing to consider is how many implements you want. A RFM would let you do a bunch of the 6 acres with the tractor, plus the 9 acres (if you get it tidied up first). Then do around trees and landscaping with the zero turn.
My fine cut mowing has all moved to a robot mower. I do fields and roadsides with either my B2601 with MMM (in the North Island), or my MX with flail (South Island). I actually like mowing with the B2601 and MMM more, but the property in the South Island is 15 acres, and I think the B would be too slow / not enough cutting width. Although the difference between 6 foot and 7 foot isn't as much as you think.....