I'm happy to report that at my follow-up visit with my urologist about kidney stone formation, while we did talk about changing diet, the primary focus was on a much simpler treatment.
While I've been hesitant about using calcium carbonate (Tums) for heartburn, and even concerned about using it for dietary supplementation as directed by the gastric bypass surgeons, it turns out that what I need to produce fewer calcium kidney stones is more calcium. That's because my problem is mostly about my high oxalate levels, not calcium levels; and in fact, more calcium is the main way of keeping the oxalate from forming into stones.
When your oxalate levels are only a bit out of range, they might make some suggestions about dietary changes, some of which are unhappy ones, but most of which are eliminating things I don't like anyway (I need an "Eat Less Kale!" bumpersticker). And that would be annoying if I had to balance it with everything else I have to consider when choosing food. But my oxalate levels aren't a few points out of the range; they're four times as high as they should be. Drinking some cola might contribute, sure, but even a draconian diet wouldn't bring me down to anywhere near within range. It's more likely a consequence of my metabolic changes than my diet. So we'll start with the calcium, which is after all not a very onerous requirement -- calcium is cheap and the only side effect I've noticed is it eliminating heartburn.
Unfortunately that also means I'm putting off having that 5mm stone removed. I say that's unfortunate only because it increases the odds that the stone will move on its own and make for a couple of days of pain, plus a surgery that happens at a time that may be less convenient. Then again, since it's a month before we can talk about scheduling it, it's possible we're going to end up talking about doing it around the holidays, which isn't terribly convenient either.