Filtered water doesn't have enough particulate in it to throw the pH off. Pure water is almost always near or perfect 7. The purity of the water does allow it to change rapidly and it is easy to have a pH problem with the stuff. The RO water, plus Cal-Mag at <10ml per gallon should hit 6.2 to 6.4ish, then your extra nutrients... as long as you are using a reasonable amount of them, should be skewing the pH that low.
You are using litmus paper. Litmus paper is not a "liquid pH tester" of the kind most growers use. Your crunchy bottom leaves probably have burned tips, right. And the top of the plant, are the tips of the leaves browning? You likely have a salt build up in the media which is contributing to the pH issue. More run off, less nutrients, would probably help resolve the issue.