Thank you all for your replies.

My plumber (who supervised the well drilling, selected the water
softener, and did all the internal plumbing) tells me that my water
softener should be able to take care of all of the iron, even though it
is just a regular run of the mill salt-fed bead-action softener. I am
challenging him on it, of course, since my research shows that
softeners are only good at removing small amounts of iron (around 2
mg/L tops). Is that true?

As far as whether or not I want to end up with an extensive water
treatment plant, my answer is no, but I also need to be able to do
laundry, so I'll accept whatever I need to do for that to happen. I do
have neighbours in the vicinity, and will perhaps knock on a few doors
and ask about their experiences.

So, reading between the lines, you folks seem to be saying that I
should be pushing for a separate iron filter/treatment unit, or
negotiating a deeper well. Is that correct?