TL/DR: My full sun front yard is being overridden with mushrooms. How do I get rid of them?
So background: Our front yard used to have a locust tree that we had to cut down 3 years ago. After a couple of years of dealing with the damn baby locust trees that apparently sprout up through the root system when you cut one down (and will even go underneath driveways to invade the neighbors yards...) we finally thought we could get a fresh start on our lawn. We Round-upped the front lawn since it was almost entirely weeds, got a power rake to de-thatch it, and planted new seed last month. And we have grass growing!
Unfortunately while examining my baby grass yesterday I realized that a lot of the brown in my yard is not just the old dead weeds/grass, it's all sorts of different mushrooms. There's a big clump of little ones growing above the remnants of the tree stump even though it's been covered over by quite a bit of new dirt. There's big flat-topped ones growing sporadically, there's little low to the grown ball shaped one, and there are little round things underneath the ground (we found a lot of these last year picking dandelions early in the summer).
My yard is south facing and gets full sun. We have been watering the yard three times a day for 15 minutes because of the new grass (cut down to 2 times a day for 10 minutes now) so the dampness is probably encouraging them but necessary for the new seed
Is there anything we can do to get rid of all these mushrooms without hurting the new grass?