Yeah, totally uninstalling and reinstalling the Steam App put the songs from RS1 back in RS2014. I could not find them anywhere on my Steam library or in the RS2014 DLC folder, so they must be somewhere else. I do not own RS1, just some DLC. I was worried I'd have to scrap up a Steam key somewhere to get access to those DLC back.
I'm glad it was worth the trouble of uninstalling every game I own on Steam. I tried one method that did not delete the Steam Apps folder or the user data, just made Steam reinstall every other file it needs, but that did not fix it. It had to be a complete uninstall. I also needed to re-enable the "JustInCaseWeNeedIt" beta code for the game before it worked again.
Thank you TheGamingMetalH
