Well it looks like you have a fine problem on your hands. However, by what you have described I don't think it's the phone system. The only thing you haven't replaced is the cabinet, however you did move card slots and ports and the problem remained. (If it was the cabinet you would have had that problem on the new ports prior ... did you move to an empty port or swap ports?)

I know you said you moved the phone back to the demarc but you haven't completely eliminated the cabling - you still have the amphenol cable and you still have the 66 or 110 block. Have you replaced those items? (I know it sounds stupid but it is a lot easier to do that then replace the entire cabinet and the problem remains.)

Good Luck - Tom