Exposed roots

[JRM]

I've got a poplar that has really started to expose its roots within the last few years. So much so that it's becoming a problem mowing the grass for fear of damaging the roots further than my teenage son already has. I think adding just enough top soil to cover the roots and reseeding is the best option, but what I would prefer is to bring in a load of asphalt grindings to tie in with the rest of what I have.
My concern is if burying these roots under that isn't the best approach for the trees health.
To be clear, I'm talking about adding the grindings in from the blue line to tie in with the rest of the asphalt grindings. The rest I would add just enough top soil to cover and reseed. Thoughts? Thank you.

 

[Raintree]

Can you split the difference? Bring the grindings to the bird house post and top soil the rest. No more than 4" in depth and no diesel on the grindings.

 

[JRM]

In other words, keep that long root free from the grindings and cover with soil. That's certainly doable.
I'd really like to take it further but the health of the tree is more important to me. It's the only shade tree in the summer on the south west corner of the house.
Thank you for your input.