Open car trailer vs enclosed

Instead of a zero turn mower consider a front mount like the old Yazoo or the Ferris. If you have to mow up under bushes and trees and shrubs you do not want to be on a zero turn because it's pulling your body into the brush or the tree. On a front mount the deck will go in 4 or 5 ft before your body starts to come in contact with the Bush or tree.
It looks like you have about a 7 ft bush hog in that Barn. Buy an old farm tractor for it. That'll save you hours of mowing time.
By the way congratulations on the purchase of the home and the buildings. Now you need to fill that Barn up with Mopars.