You can’t grind the stump away, it’s too deep. Either dig it up or just expect a pothole to develop. You did good removing the chips and backfilling with soil. 7 inches of soil is more than enough to ensure turf growth. You may get a few tree shoots for a while, depends on tree species.

 

It maybe several years before whats left decays and you get the sink hole.
I have these sink holes all over my yard. Previous owner cleared 10k ft2 and left the tree stumps and and some places the fallen tree.
I have been chasing sink holes for 15 years.
Also had to have a stump dump removed from when they built the house. That was creating a crater.
Eventually the grass will grow in.

 

yes grass can grow if grinded deep enough, i grind stumps in norfolk , va beach and Chesapeake and as long as you have about 6-12 hole , you can put dirt rite over top of the tree stump and put your grass seed on top and your ready to roll.

 

That stump is going to be there a very long long time. White Oak has a closed vascular system and as such is very very rot resistant. I had a white Oak cut down 25 years ago and the stump is still there, as good as the day it was cut. If you're buying/building outdoor wood furniture, White Oak is what you want.

On the other hand, I had an ash tree that fell victim to the Emerald Ah Borer and its stump totally rotted away in about 2 years.

Also, nut trees have very very substantial tap roots. Its big and deep and since its White Oak, its not going anywhere.

Just grind out what you want and fill with dirt. There'll be no cratering to worry about.