I'm ready for the big time. I play out around town at coffee shops, etc. You can go to a studio or do a live recording at one of those coffee shops. Are satirical lyrics commercially viable. NO, they are not.
Publishers are interested in songs that have original words and music.
If either the words or the music are not original, it will be almost impossible to market them. I would suggest finding a composer to work with, and writing new words to new melodies, or having melodies written to your lyrics. I'm writing the music and melody to words copywritten in 1998 by another person. I never met this person, and we're working together online. But together, if the song is finished to the satisfaction of both of you, you should register a copyright for the new song, words and music.