Depends on how steep and how the wetness affects traction.
Cub Cadet makes a line of zero turns with front wheel steering for slopes as well as another line that have decent slope mowing capacity. Not sure if you'd want to change out the turf tires for higher traction ones....
I suppose someone will ask why you don't buy a new rear PTO finish mowing cutter if everything else is working for you except for mower breakdowns? 7 acres is a lot of mowing any way you look at it. In most instances, cutting width determines mowing speed because you can only travel so fast on slopes without increasing the risk of rollover.
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Another potential option to consider is one of the Power Tracs like the PT 425.
T8 Class But it will take a lot of time to cut 7 acres with only a 4' cutter.
A zero turn can save time because it is easier to mow around obstacles, but if you are mowing open areas, cutting width is still going to be the primary factor in reducing your mowing time.