Looks like you have your work cut out for you. The next time you "rip it out" or even now, have some glyphosate
spray like roundup -read the instructions/warning label
- , black plastic and compost ready.
Knock it back to where you want it. Spray the roundup on the plants and surrounding ground, cover with the plastic, and top it all off with 4 to 6" of the compost. let it cook until you reach your Spring Season.
Then just dig through the compost, and plastic into the ground and plant whatever plants, flowers or vegetables that suit your fancy.
Concern over the plants, flowers or vegetables? Scroll down about 2/3rds of the above link and see ENVIRONMENTAL FATE.
Glyphosate is usually microbally broken down in 174days so letting your space "cook" from now until your Spring on September 22nd is 177days. That should be enough time to allow the little "buggers" to do their work.
If you're concerned about the compost running, blowing off or animals using it for a rest area, give it a top layer of plastic and pin or weight it down.