Invasive Grass Dilema

I had a pretty good day planned yesterday. I was going to get a jump start on winterizing my yard, cleaning and taking down the rain barrels, etc. so that I wouldn't be in a mad rush when things started cooling down in late October. Everything was going pretty good until I started some digging and began looking more closely at the grasses that were growing on the corner of the front yard.   

These grasses aren't visible anywhere else in the yard and they seemed to be getting a little out of control. I figured that I better nip this in the bud, literally, and began pulling the grass out. Some of it came out easy but I could tell there was a more significant root system than I first thought.  

I started digging and realized that beneath the top layer of soil was an interwoven network of roots. These went to a depth of about 8 inches. I figured that I better dig it all out or else I may end up with an even bigger problem next year. This is when my small weeding endeavor turned into a four-hour project.  

I ended up removing all of the grasses, along with any other plant material I had in this area. This included several nice perennials and some hostas. I figured that it was better to be safe than sorry. I have a dilemma though. I am sure there are still plenty of small root material in the ground that might grow again. What should I do to keep this stuff from growing again? I tilled the area and removed what I could and then I sprayed it with vinegar to make the soil less hospitable. I think I am going to continue tilling and pulling out any root material until I get tired of doing so and then deal with it next spring. Any thoughts?    

I now also have to relocate about 60 tulip bulbs that were planted in this area. I may even just save them until late in the fall and try to get them back in place. I guess we'll see if anything takes root between now and then.