Well, the coping damage is pretty evident - the question is, WHAT actually caused the stone to erode in such a way. What is also interesting in the pictures you've provided is that the waterfall also appears to be made of limestone as well as the horizontal pieces of stone sitting beneath the waterfall under the surface, yet neither of them appear to have similar erosion. One may assume if the saltwater is the culprit of the erosion, then the stone on the waterfall and below would also show at least some similar signs. An argument could be made the stone pieces below the surface are not exposed to as much UV or drying as the coping, but the waterfall would be hit by slash-out as well as saltwater running over the surface any time it is on. It is very peculiar there is no obvious erosion of the waterfall stones.
I'm also curious of this "SWCG = stone / equipment damage" as outside of TFP that's about all you hear. I'm also in Central TX (just NW of Austin) and am considering moving from bleach/trichlor to a SWCG primarily for the convenience factor and that I like the feel of saltwater anyway and some seasons bring my salt level to 1500 ppm + just for that reason, so why not? Yet when I call anyone to inquire about quoting install of a SWCG the first question they ask is "why would you want one?" followed by "are you aware of the potential risks for damages" or "we usually do not recommend them". Everything I've read at TFP states these fears and claims are unproven, yet many professionals in the pool industry still claim otherwise. I do have OK flagstone as my coping and spillover from my spa, so that is my only hesitation. However, my friend and neighbor down the street has similar stone and no SWCG, yet his stone is flaking and chipping in multiple areas. Point being, sometimes it is the stone and/or climate more than anything. Perhaps the physical properties of your particular coping, Dustin, is hypersensitive to even the relatively low levels of salt required for a SWCG?
Regardless, it's certainly a disappointment having to go through a renovation process. Hopefully you find a coping material where any such damage is not a concern and you're able to enjoy the benefits of the SWCG you already have.
Will be interesting to hear the results of any testing Jim performs on your coping stone.