Start by eliminating the moldy line with your RH
and let your vocal take it's place.
LH triggers the chords and the right hand is free to comp
solo and chord arpeggiate thruout the song arrangement.
You will be juggling Three things at once.
There are no rules... do it as you see fit for the song that what makes it unique.
Start off easy with songs you don't need charts,
lyrics, etc, and just play and sing without playing the melody line.
Do it every day and after a while you will get used to doing it for sure. have fun.