So, I created a new calibration profile using the transparent target that came with the scanner, and the uncorrected scans look more natural now. I have a monitor profile, but it is only a rough one, made by eye rather than using a sensor. The results look a lot more natural even with no color correction applied. Take a look at the difference in the tones:
Getting smooth tones without weird artifacts is a good start. It's probably best to work on the rest of the color correction and possible unsharp masking in Photoshop. With the black and white prints, I didn't have to worry nearly so much about color space, just getting a full dynamic range. Things get much more complicated with slides, but they have a huge amount of detail and a lot of gorgeous color, so think the extra effort will be worth it!