As soon as we got home, Brian dusted the patio with it and found that it worked much better than the stone dust. However, he also found that a single once-over with the broom wasn't going to be enough to fill in all the cracks. He'd pour sand over an area, sweep it carefully into all the crevices, run over it with the hose, and find that the wet sand had sunk into the cracks without a trace, leaving them just as visible as before. So it looks like getting them filled in is going to be a gradual process—adding one layer of sand at a time, sweeping it in, and hosing it down until the cracks won't absorb any more.
He did, however, make a little more progress toward filling in the much bigger gaps that we'd left around the edges of the patio. Since we still had plenty of fill dirt piled up from the excavation phase, he just scooped up a couple of shovelfuls, dumped it into the cracks, and packed it down. It doesn't exactly look seamless, but
at least it keeps the edges of the patio from wobbling. Eventually we'll get the whole area re-seeded, but the lady at Home Depot advised us to wait until fall if possible, because grass doesn't like to grow in hot weather. So in the meantime, we'll just have a patch of lawn that's a bit straggly and brown, rather than filled with lush, green weeds as high as our knees. Works for me.