I went ahead and enabled your post, even though it's not really the sort of question we handle here, because I think a lot of people will find it interesting. However, there are only a handful of folks here who could help, and they may not have time. As I believe you you recognize, you are working on a project where there is not a standard correct solution -- anything you do will be somewhat experimental.
Two suggestions for other places to look:
1. Search Google for forums frequented by contractors doing "watershaping" (decorative water installations). Those guys are more likely to have dealt with problems like this, than pool guys.
2. Try poolspaforum.com, which has a much higher % of pool contractors, then we do here. (I tend to run them off here, because they can't keep themselves from recommending 'pool-store' style chemical advice.)
I'll make one suggestion about the work itself, and then back out.
In my opinion, if you want "the most watertight and permanent" solution AND want to maintain appearance AND cost is not a huge issue, THEN I think you may want to consider stripping inside and top of the wall, and added a solid poured reinforced concrete wall, to which you could then re-apply the stone. Depending on what sort of gunite contractor you can find, a reinforced gunite wall could substitute for a poured wall. Poured concrete is a much more common skill, of course. Either way, you can do the bottom of the channel in whichever material (gunite or poured concrete) you use for the wall.
Two cautions:
First: Expansion joint design and installation will be critical, and few contractors (or engineers) seem to be very good at it. I don't have a solution for you, except to note that you need to look for, and find one. And once you find one, YOU will need to be on site at the critical points, to verify that this solution is installed as designed. It's picky work, and shortcuts that will last a year or two abound.
Second, both concrete and gunite contractors like wet concrete because it's easier to handle. However, in an exposed wall, over-watered concrete = porous concrete = concrete subject to freeze/thaw damage. Your weather (Providence, RI) is not as cold as I would have guessed (I looked) but it's cold enough to cause significant winter damage to wet porous concrete exposed to freezing air. One advantage of using a formed concrete wall: you can use very dry concrete, with only the water needed for hydration, vibrated into forms. Done properly, this results in a dense concrete not easily penetrated by water, and thus, resistant to freeze thaw damage. Some ongoing maintenance to the rock work is probably unavoidable.
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