It doesn't seem too promising but wait and see. Maybe your application method and "thorough coverage" was a blessing in disguise. It contains "spreader-sticker" adjuvants to lock it onto the leaf surface, good for weed control/bad in your instance. The second ingredient fluazifop (Fusilade) is the main post emergent grass killer to be most concerned about. The 4th. ingredient Oxyflorfen (Goal) is a combo post/preemergent that might also kill the existing grass, but is the pre-emergent portion that locks into the top inch of soil to prevent new weed seed (and new grass seed) germination for several months. The label shows it to be at a very low %, so you have that in your favor. The other components are broadleaf contact herbicides not to worry about.
You might get away with a deep tillage of 3 to 6 inches that would dilute that Oxyflorfen enough to allow new grass seed germination. Hopefully you have good topsoil to a six inch depth. If only 3 inches of top soil over bad fill, reconsider deep tilling it. Prime seed sowing timing is up to late September for our mid-Michigan area. A bit later might work depending on our variable weather patterns. Bluegrass takes over 2 weeks to germinate. I prefer blends of bluegrass, fescue, and rye for best pest resistance, wear & tear, less fertilizer/water., etc..
Good luck. Sorry for your predicament, but it is not permanent. You also should consider "stealing the thunder" by letting your neighbor know that you will take care of them also.