I think I just wasn't running the water enough after changing the filter. I swapped out a couple of filters and finally let it run for a while as Benjamin Sahlstrom suggests. The water may be a bit fouled at first after changing the filter, but it soon clears. It seems that all is well, although there is definitely sediment getting through:
The red in the picture above is fine silt, which settles to the bottom of the toilet tank (several months' worth). I have tested my filtered water and found that I have about 13 ppm of silica. That's definitely higher than most public water systems would have, but not all--see, for example, the water quality report for Lenexa, KS: 10 ppm silica, range 2-17 ppm; recommended federal level 50 ppm or lower. The main problem is that the silica will probably cause components in the dishwasher and washing machine to wear faster, and to some degree it may accumulate in the water heater--though the latter can be flushed.
Over time, the sediment does add up. Below is what an Aquaboon one-micron wound string filter looked like after about 4 months (with a new one for comparison).
It looks worse than it actually is. I was wondering if I had lost water pressure and so changed it; the new filter showed that it hadn't significantly impeded flow yet, even though it looked completely silted up when it was in the housing. There was a fair amount of sediment in the bottom of the housing, but that doesn't really matter.
Even after the well was refurbished, water coming out of one of the outdoor taps--i.e., unfiltered--was dirty-looking. Much of that may have been attributable to some of the supply fixtures--galvanized steel and, for two outdoor hydrants, cast iron:
All of that is now replaced (with new galvanized in the case of the hydrants), and the water is looking much better. There's still some cloudiness, but it is unfiltered, after all...