The OP wrote:

I want the vertical supports and the brackets to be as invisible as
possible. The brackets don't necessarily have to be invisible--
but I don't want them interfering with the shelf-space below.



It doesn't have decorator aesthetics, but the best solution might be to
use conventional metal angle irons to support the shelves. If you just
rest the shelf on the horizontal arm of the angle iron, it can be
shifted left-right (as you seem to desire), but will only reduce the
headroom of the shelf below by about 1/8" at most. The major problem
might be forward creep of the shelf, allowing small items to fall off
the back, or worst case - the shelf falling entirely off the bracket.
If the shelf is wood, maybe you can use thumb tacks through the holes
from underneath the horizontal arms of the brackets to keep the shelves
from creeping but allow for easy removal and repositioning of a shelf.
Not elegant, but a potential solution to your requirement.