Dealing with unwanted grass by Blackberries and Rasberries

Any and all advice welcome.
Three years ago I planted one grape, one rasberry, and one blackberry (small bushes/vines) along 50 feet of fence at the rear of my yard. The grape and rasberry have grown little / only slightly. The Blackberry has propogated into some 30 plants via underground runners (so much so that I have moved 10 to my side fence).
The grass I once wanted along the back fence is now a nuisance. I have to cut it by hand with scissors or small sheers because an electric weedeater would also cut down the blackberry vines that produce delicous berries.
So what is best to give me a well groomed look but be low or no maintenance. If I have to choose between the two on this particular subject, I prefer low/no maintenance over well groomed. The area I am talking about is a 2 foot strip approximately 50 feet in length. Here are my thoughts so far. 1) I am willing to hand pull or dig the sod once (probably take me a while). 2) If I were to put down felt to prevent grass re-appearing I perceive I will stop the blackberries which I love from further propogating. This seems bad as the blackberry canes that produce must be cut to the ground before winter/in fall, and new canes replace them via underground runners. 3) I could put down real or rubberized mulch but perceive the grass would just spread/grow through in about a year (creating more work to clean up the area if I used rubberized mulch). Regular mulch I could leave and add to next year, but perceive the grass woud just start spreading and growing into it in a year. 4) Round-up on the grass would likely kill or affect the blackberries.
Any ideas welcome. Thanks in advance.
Andy
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I would treat it like any other planting bed. Establish an edge and remove the grass. You can mechanically remove the grass or use Roundup. Roundup only works if you put it on the plant leave so it shouldn't kill the berries unless you are indiscriminate in your application method. You can use a sprayer to direct the solution to the grass, avoiding the desirable plants. Follow the direction (i.e., don't apply on a windy day). I have used a large piece of cardboard to shield plants from the spray. Another method would be to put on heavy rubber gloves and to use a sponge to apply the Roundup to the grass. You still have to remove the grass, so if it were me, I would just use a mechanical method and spot treat any areas where the grass returns with Roundup. I have a Lee Valley sod lifter that is wonderful for cutting the edge of the bed and lifting the sod. http://www.leevalley.com/garden/page.aspx?c=2&p523&cat=2,42578,40769
After removing the sod, I would use natural mulch. There is a lot of controversy about rubber mulch, and I would avoid it, particularly around food crops. Unless you have aggressively spreading grass, you shouldn't have a big problem with it creeping into the bed. I freshen the edge of my bed every year with the sod lifter and that takes care of that issue for me. To stop aggressive grasses, you can put in a barrier type edging. I think the best edging is the heavy, metal edging that is secured with spikes every couple of feet.
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