I had cataract surgery and elected to get monovision, with my left eye for long vision and my right eye for short vision. It's the opposite of what you would expect, since I am right-handed and right eye dominant, but I need good close vision for my work, and my right eye is my best eye.
When shooting the bow, I usually wear a contact lens in my right eye so I have good distance vision. However, as I shoot daily at targets in my backyard, there are times when I am too lazy to put in the contact lens, which means that I am "aiming" (I shoot instinctively) with my left eye, since my uncorrected right eye vision is a blur beyond a few feet.
I find that I can shoot about as well that way as I can with my right eye corrected. I know there are a number of shooters who shoot right-handed and are left-eye dominant, and don't even know it. When they are tested, they are encouraged to change over to left-handed shooting. Some successfully change over and their shooting improves, some don't. The point is that if your form is consistent, your brain will adjust. It is perhaps a bit more of an adjustment if your brain has to adjust when the arrow is not directly under your dominant eye, but is still something your brain is capable of doing.
Make sure that your eye is focused on the target, and not on the tip of the arrow or your hand. Focusing on the tip of the arrow could lead to the type of errors you have experienced.