I'm archer also I'm amazed you get spotted. Are you using steady aim? If you are then if the eye starts to open if you zoom in to slow down time you can get shot off before it opens and still get multiplyer.
I got my crosshair disabled, and same with the sneak-eye. It gives me more immersion. I also disabled enemies on the compass, so no red dots spoiling me where the bad guys are.
As I got my music volume barely audible, and voices and effect maxed, I rely only on what I see from my first person view, and what I hear. Lets say I have to enter a room (in a fort). I approach slowly while checking for dark places where I can hide in case someone comes. If I get in a light area and it happens to be an enemy around, I won't notice that he noticed me because I don't have the eye, so if I hear "Is someone there??" I will just stop and go back to that dark place I spotted, if available, or else I will just try to spot the guy as fast as possible, aim, shoot and try finding a dark place for the other guys that will come after hearing the noise.
It's basically the same all the time.. it's more fun when a big guy is around, because it requires more than 1 or 2 shots, so I have to find a good place to hide. Sometimes my only option is to launch the first attack hidden, then shoot a couple more while he comes, push him back with a shout, and pray for a paralizing shoot, so I can finish him off. If those big ones get me, I have few options. I go overweight most of the time so I can't run away or fight in a fast-FPS-Quake-style (I don't like it either). They just kill me in a couple hits. Similar with those bandits dressing as imperial soldiers. I either kill them from the distance, or I'm done.
Currently I use a normal ebony bow with dwarven arrows (level 39).
EDIT: Yes, I have steady aim (got almost all archery perks), but I only use it with fast-moving enemies, or when several come towards me, so I have a chance to take them down before they get too near.