I would suggest when shooting a bow use what ever eye is dominant. Don't go by what hand you use most often. I am left handed but right eye dominant, so I do most everything right handed that involves sports or shooting.

Something to keep in mind, if you shoot pistols right handed, this is the hand you would have extended with a left handed bow. With a bow it is opposite. A right handed bow puts the actual bow in your left hand and you draw with the right. If you have no previous experience shooting a bow learning to shoot left handed should be pretty simple. Now if you have been shooting for while and tried to switch it would be pretty difficult.

In your case I would highly recommend a left handed bow and decent instruction on form and shooting. CAN you shoot a right handed bow with your left eye, certainly you can. I have seen People shoot them missing an arm and using their teeth. Anything is possible if you try. However at this point I think you would be better off just learning to shoot left handed.

I would also suggest the compound over the crossbow. I have nothing against them though. I have owned both and actually feel the compound is the better weapon in the long run. There is just more you can do with them. They are more complicated to a point, and require more practice but the pay off worth it in my opinion. Go somewhere and shoot both, or be around people shooting both. You will see the differences. Especially considering it's not legal in your state during archery season. I doubt the DNR will grant you a permit because of vision loss in one eye. They might though. Normally it has to do with a strength or lose of limb disability. Where you physically cannot draw a regular bow.

Good luck, let us know what you decide.

Paul