Dave; Your journey for the past two years sounds a lot like mine. I started with a RH compound from a pawn shop, then got a LH Bear Grizzly recurve. I found that I really like shooting arrows. :-)
Now I have two compounds (LH and RH) and 10 LH recurves and 5 RH recurves.
I am LH and right eye dominant. I shoot the LH bows (recurves and compound) split finger and bare bow. I shoot the RH recurves barebow with a release, and the RH compound with sights and a release.
I like the balance it gives to the muscles. I like using similar draw motions with the respective sides of the body.
I like the improved coordination I have gotten by learning to do fairly complex motions with both sides of my body. Even the simple act of nocking the arrow was intitially challegning but now feels very natural on both sides.
Whatever approach you take, enjoy the journey.
Jeff