Step 1. Remove the residency requirement.
All schools require 1-2 years of classes at that school no matter how many total credits you've taken. I can understand that Harvard would not want you drop in for one class and then claim you have a Harvard degree. Fine. If you meet the credit requirements, but not the residency requirements, issue a non-school affiliated degree, a G.E.B.
Step 2. Establish a national curriculum standard for courses required for G.E.B. majors.
Just expand the General Education Requirements are already in place for a two year degree/transfer. Require the GRE general and subject area to graduate.
Step 3. Accredit free and low cost online class options for all coursework required for a G.E.B.
Lecture sections on YouTube. Pick your professor. Feynman for Engineering Physics? Neil deGrasse Tyson for astronomy? Maybe Tim Wilson for Philosophy 101?
Lab sections by simulation, kit, or maker space at community colleges. Discussion sessions by Skype, UberConference, or Meetup.
Tests proctored by the same system used for online high school classes given by BYU (which if you have a H.S. kid, are awesome). A proctor can be a teacher or librarian. Tests are sent to the proctor, given under supervision, then returned by the proctor. Or setup testing centers at community colleges.
A degree becomes affordable by breaking up the University cartel. removing rules designed to protect the institution at the expense of the students.