Thanks, rolig. That's what is done in the text—the first appearance of "Quaker" is preceded by "Society of Friends" and in fact Quaker is parenthetical. But since it is used in so many places, it's impossible to replace every instance with "Friend" (nor is it desirable to do so, for clarity's sake).
I went to a Quaker school and for a number of years attended a Quaker meeting (i.e. what Quakers call church), and I never met a Friend who was offended by the word. They even use it regularly themselves, though Friend is the preferred term. Still, I have heard Friends speak of "Quakerly" behavior or "Quakerly" ways of doing things. The organization's website, www.quaker.org is here, and they use the word throughout. Also Quaker blogs are to found at Planet Quaker. So I think you can use "Quaker" safely, but somewhere in the text it should be made clear, as reesetee says, that this term refers to a member of the Religious Society of Friends".
In my work, I've never had anyone suggest a problem with "Quaker," even though, as you point out, it was originally a pejorative term. I think it's generally accepted today by most. However, as you also point out, it's not the preferred term for Friends themselves. In such cases, I go with the term preferred by the people described--in this case, Friends--even if "Quaker" is acceptable.
Of course, the initial cap helps, but could you possibly take space to spell out "a member of the Society of Friends" and then simply say "Friend" or "Friends" in subsequent mentions?
Okay, I know that Quaker is not the preferred term for a person who is a member of the Society of Friends. I know that they prefer to be called Friends. And I know that "Quaker" was originated by people who intended to belittle the religion and its practitioners. I know that the guy on the oatmeal box is not the ideal.
However, I have been under the impression for many years that "Quaker" is not, any longer, exactly a pejorative. In fact it seems to be most frequently used, in the texts (history books, etc.) that I've encountered, in instances where "Friends" would make little sense (e.g. to students who don't know what Quakers are).
But someone just told me it's insulting and pejorative. I'm guessing that those who have the power to approve these (history/educational) texts I'm editing are going to insist we call them Quakers. Among our enlightened and helpful Wordizens, is there anyone who can shed some more light on this issue?