I'm a lefty to the core. My right arm is a useless appendage for most activities. Being a lefty though I can't try bows in most cases so I've taught myself how to shoot right handed for this purpose. I've gotten pretty good at it and I'm sure if I had to I could hunt right handed. If I can switch after 20 years of shooting lefty I'm sureyou could learn to shoot left handed.

If you can't you can try shooting instinctive as that is not eye dominated, or use the crossbow.

Crossbows are a good altermative as long as they are treated as bows and not short range guns.

This is a foolish statement. A crossbow is not just like any other bow any more than a compound with let-off and sights is just like a recurve or long bow. They are very different. Not better or worse, but different.