If you do use the melt method, keep in mind you will have burned dirt that won’t grow grass worth beans for awhile unless ou mix in some stuff from a garden shop.
The melt will burn the nutrients off and leave sterilized bits behind.
So come spring you’ll have to mix in various stuff and reseed the grass, but at this point with frozen ground you’ll be doing the reseeding in spring anyway after digging no matter what.
Not certain the ground composition near you, so you’d have ot check with the garden shop for what you’d need.
Thanks. No lawn.