FR would seem to fall under the "not-for-profit educational corporation" category. This, of course, depends on the particular state "definition" of such. The California Code is at
this link.
An educational corporation simply provides some type of "educational purpose"; information dessimination is usually one such purpose.
Additionally, a corporation can be "initiated" in any state (preferrably one most accommodating) and then "registered" in the state where the actual "head quarters" or operation takes place. The two primary codes are the State corporation code (where the corporation is born) and the IRS Corporation Code for tax/tax-exempt status.
Having run two non-profits, I would say your information is right on target.
"Education of constitutional and conservative principles" would pass muster as a mission statement for the IRS as a non-profit. Just check the box on the IRS form that says: "Educational," and provide a one-paragraph narrative of the mission statement. The downside to a non-profit is the requirement of a elected board of directors, and so on...