Generally, attempting to plant mowed turf is doomed to failure.
I understand that fire is used out west in the high grass prairies to prevent the prairies from becoming uniformly grass.
You can try tilling, but I've always found a tiller to be generally useless.
At my house, a shovel works very well.
At your house....
Maybe get started last fall, by leaving the dropped leaves on the ground to smother the grass.... Or smother it one of the other ways, like cardboard or mulch or whatever.
Waiting until spring.... Not so good.
