Actually, this turned out to be the most straightforward part of the whole project. Yes, we still had to use the wheelbarrow and the ramp to haul stone dust down to the patio, but the dust was a lot easier to shovel than the gravel. We did inevitably find ourselves picking up a few bigger bits of stone in each shovelful, but we just picked them out by hand and dropped them into a bucket. No doubt we'll find a use for this leftover stone eventually—perhaps as a weed barrier in some part of the garden.
Brian decided to put down the layer of stone dust using a slightly different method from the previous stage of the project. With the gravel, we filled up the entire cavity first and then worked on leveling the piles. With the stone dust, however, we dumped just a couple of loads at a time and then screeded them, using short lengths of two-by-four and molding to create a reasonably level surface. This way, we didn't need to stand or sit on one dust-covered area in order to smooth out the area next to it. We were also able to keep an eye on the thickness of the sand layer as we worked and make sure that it was at roughly the recommended 1-inch depth. (If we'd filled in the whole thing at once, we wouldn't have been able to see where the top of the sand was in relation to the gravel underneath.) So we started at the far end and worked our way back to the near end where the ramp was, until at last we could remove the ramp and dump the last loads straight into the pit.
This whole process went much faster than I expected. The only complication we encountered was that as we swept our screed boards over the dust, they'd occasionally knock loose a buried piece of gravel, which would leave a furrow in the dust layer below. So we'd just pick these out by hand, toss them in another bucket, and fill in the gaps with more stone dust. We were actually able to fill in the entire area with stone dust by the end of the day on Friday, and on Saturday we just made a few adjustments: checking the level, removing the corner stakes, adding more dust where needed, and tamping it down. In fact, this whole stage was done so quickly that I never managed to get a picture of it while it was in progress, but I did get a shot of the the end result: a (reasonably) smooth layer of stone dust, neatly tamped and ready to accept the first pavers. It's almost a patio!