Interesting about the stand-up mower. I can see where much more weight is put on the drive wheels, which may be what causes your problem. I've never experienced divoting in my Toro zero-turn with a seat, which more evenly distributes the weight.
Plus when I'm mowing an open lawn I generally go around the house once to get a couple-foot-wide path, then come at it at a 90-degree angle, say from paved the parking area to the house, dividing the lawn into two or four segments so that I'm actually driving a continuous rectangle rather than adjacent rows. I love that mower! It's only flaw is going down a steep slope at the back of the house, with the risk of running into a tree or a bit of granite ledge from the last Ice Age. We should have put a swimming pool there, to get rid of the sharp drop.
I should draw you a diagram, but let's say the front lawn is 80 feet wide. Okay, I divide it into two segments. Starting from the parking area, I first mow at 20 feet, turn right at the house, go to the end and turn right, drive along the parking area to the unmowed lawn just beyond my first cut and turn right, drive to the house and turn right. Rinse and repeat. In about eight minutes I have mowed the first 40-foot width, then I do the next one and the front lawn is done. The sides and the back lawn each take about the same time, so call it three-quarters of an hour all in.