What are the current options for short crank arms? I have knee problems, and I've noticed that the seat position that makes it possible for my leg to not be absolutely straight at the bottom of the stroke causes my knee to pop up a bit higher than my hip at the top of the stroke, and I can feel it. Biking should not cause me more knee pain than downhill skiing, but it does. I think that switching to a shorter crank would help. For my leg length, about 155mm-160mm looks about right, according to the various calculators I've seen linked here. 

However, I'm at a loss for actually finding said crankset. Has anyone run into moderately-priced (under $400) cranksets that are either built with short cranks or have them available to be attached?

I'd prefer a 3-ring mountain bike set with fairly wide gear spacing(?), since I'm more of a woods and gravel trails tourer than road racer, and this place is really hilly :)

Alternatively, are there any ready-made women's/older children's bikes with crankarms in this range?
There aren't many options out there for cranks shorter than 165mm. Your best bet is to buy a set of longer crankarms and get them shortened at a service like Bikesmith Design.

Also, if you are legitimately having knee problems, I'd suggest that you find a professional fit service in your area and have a fitting done. The length of your cranks may not be the issue, but it may be the size of your frame, position of seat, etc. Online calculators can be good, but a professional service will certainly address these issues in a more targeted way and perhaps save you from spending unnecessary money, modifications to parts and perhaps save you a lifetime of pain or discomfort.