Keep your left hand low and circle to your right, away from his right hand. Move into his left and make him throw it. I'll bet you that he's not a natural southpaw; I've never met one that didn't wing that left. This guy doing so much right handed- slapping your left, then jabbing or hooking- tells me that he, like Michael Moorer, is naturally right handed. By moving to your left you are playing into his strength.
Circle right, keep behind your left shoulder, make him punch across himself with his right hand. When he throws his left hand, throw your left hook. (See Yori Boy vs Marquez...Raul Marquez) Or get under it and bring the right hand uppercut to his body or chin.
Test his left hand; make him throw it. I'll bet you it ain't his strong one, and a southpaw with a weak left hand is a victim.