Yes, you can get rutting on slopes, mostly from wheel spin while turning. Measure the Narrowest Gate you have. Subtract 2"
Go to your dealers and ask about Riding Lawn Tractors. Lift up the Grass Chute and measure across the deck noting clearance. Then get the appropriate size deck. A JD La-165, or that size range, 17-20 HP should serve you well, 42" if you have lots of obstacles. $10,000 cheaper and much more versatile than Zero Turn. You can tow small trailers easily and also a Wide Sweeper. roller etc. Keep in mind gate width. I use an X320 48" 22 HP on my half acre . Cutting time 25 min. Watch for used riders $250-$500. Check Forward and Reverse after hot before purchase if it is an automatic. Check all gears if it is a used Standard.
Mine has a 3 blade deck that conforms very well to uneven ground. I have installed some custom features. All my photos are too 'large' to upload here. WTF?