i may be too late with this, but i thought i might be able to help. you really don't need the "landscape cloth" layer, and in fact your suspicion that it inhibits the compaction is correct. the compacted dg will tend to break up as it slips on the landscape cloth and be less stable than if it were just on a base course.
i am an architect and have been working with landscape architects on decomposed granite paths, parking lots, patios, etc. for years. we have always had problems when the contractor insisted on using some kind of weed prevention cloth layer. the first thing you need to do is REMOVE the grass - don't just kill it. if you leave the dead grass, as it decomposes it will create voids that will cause settlement. the best way to install dg is to compact the base soil with a plate compactor, lay down about 4-6" of what is called aggregate base course or "road base" (assorted size gravel with some fines) and then compact that with the plate compactor, and finally the dg (about 3 inches thick) and compact that too. if the base is properly prepared and everything is compacted that way, it will be a rare and hardy weed that ever makes it's way through. make sure that the surface is crowned slightly or else slopes one way or the other. dg will absorb water, but it does so at a semi-slow rate, and you want to eliminate ponding.
you don't really need any kind of stabilizer or binder unless you want to support vehicular traffic. if you do, i don't know that you can get it at lowes or home depot. we usually have it supplied by a company called Stabilizer Solutions (out of Arizona) but they pre-mix it into the material and truck it out to the jobsite (cross country if necessary). not really good for do-it-yourself kind of jobs...
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