Yes, you may be overthinking this at your level of experience. Don't worry, most competitive shooters do this, changing chokes, changing guns, changing shooting style, changing ammo, changing glasses, even changing their socks or shoes, always looking for one more target.
The beads are for alignment when mounting the gun to assure that your head is properly positioned. They are NOT sights like on a rifle. In essence your shooting eye acts as a rear sight.
Rifle shooters learning to shoot flying targets with a shotgun tend to try to freeze or stop the bird, a sure way to miss behind. Your target is moving, your gun must continue to move as well with good follow through.
Proper gun fit means nothing with a rifle because you can position your head anywhere to align the sights. On a shotgun, gun fit is everything. You weld your cheek to the stock in exactly the same place every time and if you are looking perfectly down the rib, when you swing the gun to and through the target with your fore hand you just need to get your trigger timing in sync and the hits will come.
Close your eyes and bring the gun to your shooting position, then open your eyes. If you are looking straight down the centre of the rib and can see just a little of the top surface you would hit what you are looking at and the gun fits you quite well. Do this 10-20 times to check for consistency . This is just a rough and dirty check for fit but it can point you in the right direction. If the fit is poor you will need a better fitting gun to hit consistently. Although lots of practice with this gun will enable you to adapt somewhat, you will never shoot it as well as one that fits properly.
Both eyes open is better for shotgun shooting because with one eye closed you have no depth perception. This is particularly important in sporting clays and hunting. Some trap shooters do very well closing one eye or using something to block the weak eye such as small patch on the shooting glasses or a full patch, some close an eye, some shoot both eyes open or one squinted. There are excellent shooters using all of these methods so none is the best overall for everybody. Skeet is a very quick close range sport and using both eyes is an advantage . In sporting clays and five stand with their infinitely varying target presentations depth perception becomes more important to establish target distance, speed and flight path. Most of the best sporting clay shooters either shoot with both eyes open or squint the off eye. Hunting, with it's completely unpredictable targets is usually better served by shooting instinctively with both eyes open, with maybe waterfowl being an exception.
Above all, learning to hit flying targets with any consistency usually takes practice, practice, practice, just like golf, fly casting, curling or any other sport involving motor skils. Good luck and have fun.
