That is WAY too much ground to mow with a riding mower. Sell it and get a machine with larger wheels. You didn't say where you were located but my guess is that you have gophers, moles and frost heaving. Those are natural things that take an entire grounds crew to eliminate. You also didn't say what sort of seed you planted, but I bet it was rye. Cheap but not a good choice for a lawn of six acres. Bluegrass would be the way to go.
The zero turn I use is a 60" Z900 commercial series from John Deere. It's built to withstand heavy usage and mow acreage. Rear tires are 24x9.5-12. No suspension seat. I am looking into suspension seat options. Freeze and thaw cycles must have come into play to make it this rough. I'm mowing at no more than half the machine's capacity and I bounce off the seat.
The grass seed used was a mixture of 30% fescue, 25% bluegrass, 55% rye.