I would bet on the water heater. Everywhere you complain about rust is from a source that is using hot water, and you said your well tested out with no rust. The softener is going to be upline from the water heater, so any tests there are negative as well, right?
The shower uses hot water, ergo tub, curtain and your curly locks.
I would never trust a water heater that old. The other reason is one of logic. If it was the pipes, in order for your water to collect a noticable amount of rust (enough to turn the color of your hair and the like,) it would have to be able to draw that much rust from the pipes as it goes rushing by. It doesn't sit in the pipes long enough to collect the rust, so the only rust you actually pick up from the pipes would be what you get when you first turn the water on. (test this by running two glasses of water from your tap, a "first glass" and again after 5 minutes of running the water. You should be able to taste the difference if there really is one.)
What is far more likely is that the water heater hasn't been drained of its sludge over the years and the flow of water into the tank as it gets used stirs the rust up into the water and you end up with it in your towels. (By the way, you don't have to wash your clothes in hot water, and its expensive.)
I bet its the water heater. If your plumber is still scratching his head, you might consider looking for "a second opinion". (and a few references)
The only other possibility, like bc describes, is your pipes. If they are copper then its not them. However, if they are galvanized iron or steel, then you may have an issue there.
Here is an easy way to check out the source: Take water samples from several different sources, tracing the path of the water to each source. Start with the well, then test between the pump/pressure tank combination and the house (it could be the pressure tank, but I doubt it), then an outside faucet before the softener, after the softener but before the water heater, then test both the cold and hot water from a couple of different taps.
This should locate the offensive part, but again, I think its the water heater.