Try looking at where the roots are aligned with a tree.
Go as far to the tree as possible, then use a very sharp handsaw, and
cut down into the turf, at right angle to the root, at some point you will meet the root, cut through, if it's not to deep to manage, dig down to expose the cut, and maybe rope the end and pull it out with some form
Of traction.
Then make good the ripped area, back to lawn.
I have done this with success on more than one occasions, just don't bite off more than you can chew.
Good luck witch ever way you go.
John.