The problem of the quackgrass/crabgrass may be a blessing in disguise - it will force you and all of us to move in a direction of gardening that we all should be following - I have the same problem in four of my raised beds and the pathways. You can dig all the way to China, and it will come back even stronger - the more you dig, the stronger it will grow - I tried it.
I was not willing to abandon the beds (even though I have space in other parts of the farm) and I was not willing to keep digging.
I have used heavy mulching, in place composting and the use of green manure crops - it seems to be working.
In the fall, vetch simply scattered (no digging) on top of this type of grass, does very well. As the crabgrass begins to "fall asleep" in the late fall, vetch simply scattered on top of this grass will do very well, it grows and covers the whole area - in the spring you can use a knife to cut down the vetch, and simply lay it on top of the bed - the quackgrass will stay put underneath this heavy layer of mulch.
You can plant your vegetables by opening small holes in the cover material - over time a thick layer of
compost will develop and the quackgrass will be less and less of a problem - if it begins to poke through the heavy layer of mulch and compost, just gently pull it out.
The roots of the quackgrass which have formed a mat under your soil will die down and provide nutrients for your plants. You can add materials to be composted in this bed, dry or green grass, some soil, manure etc. Keeping 6 to 8 inches of mulch materials on the bed is a good idea - it will constantly be breaking down and improving your soil.
When you harvest your vegetables all residue should be returned to the bed, and you should have something growing on the bed all the time.
Quackgrass and crabgrasses show up for a reason and will go away when the cause is removed. This approach eliminates the need for digging, reduces weeding, reduces water requirements and eventually will not require any manure - or so I hope.
I am trying this approach, because I see it as a waste of time to keep fighting nature.
This has been my experience so far.
Kostas