Looking for Advice on Selling Songs

Rejection would be motivation, its the Red Tape that kills me

I've been doing alot of studying and writing, and more studying and more writing.  It is apparent that so many artists these days are in need of songs or lyrics.  I happen to have a surplus of them, and I am constantly writing.  I have quite an extensive catalog of unreleased songs.  More than I could ever release or perform on my own.  Some of which I feel are very good but don't fit my personal "Style", so they never will see the light of day.  This led me to thinking about selling songs to other artists.  I've been trying to find a way to get started in this process.  It seems as though most places will not even take submissions period. If I was getting rejected because my songs were not good enough, that would be something I could use for motivation to write better, however  It is a little frustrating that I can't even get my work pitched at all.  I have tried contacting various publishing companies, and most will not even listen, or view your song.  I am looking for any advice on this process that can help me get started on my journey to selling songs, or lyrics to artists who want to spend less time on the writing process.  Anyone have any advice to getting my foot in the door?