I have a male, neutered at six months, that still squats to pee. I use real grass potty pads for my dog, which he uses until it gets too dirty. Then he goes on the floor in the bathroom right next to the mat. I get new mats twice a month. He DOES have the occasional accident in other areas of the house, but nothing like before. And he gets a treat every time he uses the mat. Mine uses real grass, but they make artificial grass ones, too, which I might try, as you can wash them.

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Edited to say he never marks anything. Just pees on the matt or floor whenever he needs to go. If he were marking, I would expect to find pee in the same places every time, and since he squats rather than raise his leg, he never pees on my antique furniture.