We've had better luck using layers of newspaper, cardboard, and old carpet to initally kill the grass. We put welded wire cages over the barrier, fill it will all of our fallen leaves, leave it for winter, put on top soil. We remove cardboard or carpet but leave newspaper underneath. In spring perennials can be set into the top soil or seed can be sown. We have cleared several extensive areas of grass using this method. Burmuda grass roots can go down several feet and spread. We try to keep a somewhat clean area between grass and beds, or keep it in a conditon to mow the grass closely along the borders. We have used landscape timber secured with rebar as garden and path edging. We use the ground barrier cloth underneath cedar chips for pathways. The cedar eventually will deteriorate and we remove and replace it about every other year to use as mulch in the beds. Our gardens are becoming more and more low maintainence with time but there will always be weeding and grass invasion. We know that if we neglect anything for long the weeds and grass will take over because there is so much of it in the environment around us. However, it is easier to remove from the soft organic earth than from the chuncky rock subsurface. We have also tried using hericide on grass but not with much success. Killing it by smothering has been the most successful way of keeping it out of our garden spaces. Much of our property was initially rocky, grassy, hard to mow slopes and terraces. EP
Example of a previously hard to mow steep slope, now a comparatively low maintaince area:

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This is not an organic solution, but Ortho has a product called "grass be gone", should say "SAFE FOR LANDSCAPE USE" on the front. It's not cheap, and it's not instant, but it does kill out bermuda in flower beds and doesn't kill the flowers. In my iris and daylily areas I think I had to spray at least twice. I recommend it for areas where it is impossible to get it all out.

Lisa