Seems like canting the bow would result in the arrow falling off the shelf pretty regularly since it would end up on the bottom. If you shoot with the bow straight up and down, it might work, but remember the arrow will be behind the riser to your eye too.
I think it would feel pretty funky in your bow hand too, as most center cut grips are designed for the thumb opposite the arrow.
I'd definitely want to try before buying a bow designed for your non-dominant side. Why don't you try shooting it left-handed? I think that would be way more successful.