Yes, Virginia, there's such a thing as too discrete
I did, in fact, buy myself a camisole (in a modest style that, naturally, the vendor no longer sells). But I ran into the problem that a lingerie saleswoman had once explained, which is that women's "basics" are generally made for the majority of women who are taller than I. Consequently, we shorties have no choice but to tighten the straps (or have them shortened)--and when the straps stretch, the garment no longer fits properly. After a number of months, I found myself pulling the camisole way down in the back to force it to stay up in the front.
So I gave up and bought myself a couple of sleeveless cotton tank tops. This style is just about perfect. The non-stretch straps hide that other set of straps, and anything else above the "support system" that I don't want to flash in public, while still being barely low-cut enough, if I tug the tank down a smidge in front, to remain hidden under those blouses of mine that have a lower second button. (I refuse to choke myself by buttoning all the way up, but neither will I leave more than one button unbuttoned.) Since I bought the tank tops in "Light Eggplant," a pale purple (no longer available, naturally), they're also practically invisible even when worn under a white blouse, while still hiding the view completely.
Unfortunately, that near-invisibility creates a different problem--if the blouse gaps open between buttons, it's almost impossible to tell that what's directly under it is a tank top, not just my bare skin. I give up. This tzniut/modesty business is more complicated than I thought.