1) I've read that the nutrient solution in all methods of hydroponics must be flushed and replaced every so often. Is this because the ratio of the different dissolved nutrients gets out of whack by selective absorption from the plants?
Yes.

2) I know the standard for hydroponics is to water with a mix of all of the necessary nutrients, with air being supplied in one of many different methods depending on the type of hydroponics you do. However, would this work: given a requirement to have 1% of your solution be Nutrient A, 2% of the solution Nutrient B, and 3% of the solution Nutrient C, to water for a short period (say, one hour) with 3% A (nothing else), then with 6% B (nothing else), then with 9% C (nothing else), then go back to A?

Don't know. I use a run to waste system that utilizes a 55 gallon drum of concentrated nutrient and a venturi type injector to "water" my plants that are growing in pine shavings in special grow bags. It is working very well. I would suggest trying your idea with a small 2-4 plant system. Good luck, let us know how it works out.

Thanks; I'll probably do just that. :)

In case anyone is curious, I've put the basic schematic that I had in mind (very simplified!) online:

http://www.daughtersoftiresias.org/images/watering.png

Basic idea is that, if there's only one "nutrient" in play at a time, you can reconcentrate it with reverse osmosis (any temporary supersaturation will recondense around the undissolved nutrients; they're effectively seed crystals). The water that passes through goes back into your water tank, your nutrient tanks remain at 100% saturation, and so the system can measure out proper mixes every time it changes nutrients.

The diagram skims over some things (pressure regulation, freshwater intake, backflow through the filters to keep them clean, wiring and control, etc), and isn't to scale at all, but it's a general idea of what I was thinking of. I'd have to look into how well it applies to the general case, though... salts with chlorine ions wouldn't take well to RO, for example. Probably want a sediment trap, and might need to add an activated carbon filter before the pump to filter out organics.

Once again, thanks for the feedback :)