I have been using a multi method aproach to get rid of my quak grass . I use an 18 inch physical barrier to block as much root spread as possible while I work on digging out other areas. I smoother other areas with a tarp. For new areas I plan on developing for future no till , I actually till every time it gets 3 blades of grass to exhaust the root system as much as possible for a whole year before I begin ,raking out as much root every time I till. Then I dig in the 18 inch deep barrier to prevent grass from working into the new area. I mow very short in early spring and fall during the main cool season growing season and then add organic fertalizer and water a few times during the summer to help the summer cover crops get stronger to compete allong all edges of my gardens . The other thing I do with tarping is pull it back every time the grass has dyed back to let it grow 2-3 leaves before recovering it to make the roots use their stored sugar rather than just going to sleep.
This grass is a beast but it can be managed with lots of work.
My friend has used the 18" deep barrier and has prevented invasion into his garden for over 8 years now. The depth of the barrier is dependent on your soil type though so you may need deeper if you have wetter clay type soil.
