What is the plan after is the real question. Is it gonna be soded? Made into beds? I would spray the scrap out of it and do the job 2 weeks later. Then you can string trim it flush and till. Won't be fun but I would get it dead first.
The other option is to make it look right spray it with a selective herbicide to kill the grass growing in it. Then trim it with a string trimmer and treat with pgr after it starts growing in a couple weeks.. Atrimmic works well on that. Will fill in nice but not grow like mad for about 10 to 12 weeks. Then trim again and treat and you are good for the season.
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