Ideally I would like to have this an all-grass yard. I am looking out a window of the house and can't add soil on top or the grade would point towards the foundation. All these rocks are 3-6 feet from the house.

I was wondering if I could fix it by breaking up the first 4 inches of all the rocks and cover with soil. Would I need more than 4 inches, less? I would drill into them using masonry bits and drop in some of that expanding foam stuff and remove the excess slowly over time. There are about 10 more rocks not shown. Could this be done DIY over the course of a spring/summer/fall? Would it even work? Better options?