I shoot two eyes open with the right being dominate, left just focuses on the outline of the target to make sure I'm in the area I need to be and seeing the target correctly.
I have never used a magnified sight either but I used to go to a lot of competitions and a lot of the competition set ups use magnified sights.
You also said you use a longbow? Not compound?
Regardless it sounds like you either need to get glasses or you need to relearn how to shoot your bow, they make a large hole 3 string peep which I use for low light conditions but I have shot a compound bow with no peep and no sights accurately before as a kid fooling around so it's all about repetition. I shot that bow like you would a recurve aiming down the arrow, not nearly as accurate but it would have been good enough to kill a deer on the ground at 30yds.
I have been a hunter most of my life and I can speak for many of us that we practice so the animal dies quickly and with the least amount of pain as possible. I don't trophy hunt, if I get a buck cool, if not my freezer is number one before a trophy on the wall.
In my mind whatever you decide to use I would suggest you thinking about the animal first and not your pride, if your not confident with your bow please don't use it and buy a cross bow with a proper scope.
When you take a deer into the Processer is he gonna care what weapon you used to harvest the animal? No he will judge you on how clean the shot is.
I own both a compound and last year I bought a Excalibur Exocet 200 for one particular stand that's in a hot location but you absolutely can not get away with ANY motion but I shot a doe with that bow and center punched the heart in a 15ft treestand at about 25 yards. That my good sir is why we practice. That's by far the most accurate crossbow I have ever had the pleasure of using, I can literally split arrows one after another at 30yds.
So whatever your reason for hunting, meat or sport remember that the animal comes first, you need to decide based on what's best for the harvest and not what's best for your pride.