I need exclusive rights to my song to publish - How do I do that if I leased a beat?

You ARE the exclusive rights holder of your SONG... just not the underlying BEAT.  Two different things there.  It's just like a movie.. that Disney movie may be exclusively licensed to Disney Plus, but some of those songs in it are definitely non-exclusively licensed and used in other projects.  You have nonexclusive rights to the BEAT, but you have exclusive rights to your SONG.  Hope that clears up any confusion there!  Go get it!