My take on these cases is a little different than what a urologist might say, but not without research support. It sounds like, given the diet change, the initial assumption was that this dog had calcium oxalate stones, but then when struvites were identified, the diet was switched to c/d. The fact that cysteine stones are observed as well, though, suggests the dog has a propensity to stone formation in general.
This is important in interpreting the cysteine stones. The recommendation against breeding comes from the understanding that cysteine stones arise from impaired transport of cysteine out of the renal tubules due to an inherited defect in the receptors involved.
Given that many stones form in this dog, however, an alternate explanation may be that cysteine levels in the urine are in fact normal (a certain amount of cysteine clearance is expected), and that the real problem is a propensity to stones of any type.
How can dogs get a general tendency to stones? This is a matter of speculation, and not really addressed by urologists at present, I don't think. Crystallography suggests, however, that all stones start with a protein nidus. How, then, would the urine be seeded with protein? Other studies in dogs have shown that processed highly assimilable high energy diets promote tendencies to systemic inflammation, with the kidneys being the very first site where organ damage is seen (presumably from over-exposure to inflammatory mediators because they filter so much blood so quickly). If these mediators damage tubules, they can both impair tubule function in general, but more importantly, seed the urine with protein.
The only way to avoid this phenomenon is a real food diet. I'd go back to the raw or the homemade diet to arrest this process. Excessive protein restriction does not work to prevent calcium urolithiasis in dogs anyway, and is tried only because of the calciuric effects of very high protein diets in people. Normal protein levels are not problematic in people and neither should be problematic in dogs. The slower digestion rate should, however, lower insulin levels and stop the post-prandial inflammation that then damages the kidneys.
As to a formula, given the breed, tongue and pulse, I'd wonder about Dang Gui Shao Yao San. Although you're not seeing calcium oxalate crystals here, there's no reason they won't show up next, if my speculation is correct. DGSYS will unwind the tendencies to post-prandial inflammation (aka Dampness), while supporting normal renal circulation to resolve chronic inflammation.
As to existing stones, they tend to slowly dissolve under the influence of the diet change and the formula. The high methionine in a normal protein meat-based unprocessed diet should prevent struvites from occurring.
Hopefully this helps you out. Please let us know how it goes