(Just some mish-mash at the moment...)
One option to consider is open licensing (see http://www.eff.org/IP/Open_licenses/eff_oal.html & http://creativecommons.org/). I'm certainly not against artists who pursue receiving payment for their work through traditional means; after all, I receive traditional payment for my work as a programmer. But I like releasing my stuff (what little there is) under these licenses because then anyone can freely use it as they see fit. If not many people use/need it, then there's no real financial issue. If many people do use/need it, then I trust God to provide other options to financially support me to continue on with the music (including, of course, changing to a non-open licensed financial structure...)
This notion has become popular in the computer world with open licensed code -- some organizations are now full non-profits (http://www.perl-foundation.org/), receiving donations to continue their work -- much like a missionary lives off the support they receive from others in order to do ‘free’ work.
Obviously many who minister full-time have finances working one way or the other (or both).