I was going to suggest hawk decals but when I googled I found a few interesting pages that suggested that they don't always work eg "Note, however, that birds will attempt to fly through any space larger than 3-4 inches, so decals and strips must be close together over the entire surface area to be effective." However, looking at the reviews, some people do seem to find them effective - it must depend on individual situations... and perhaps you'd find them just as distracting as the disc things.
"Position your bird feeders, birdbaths and other attractants half a meter (1.5 feet) or less from your windows. From this short distance, birds cannot build up enough momentum to injure themselves should they hit your window." flap.org
I recall reading about a film that can be applied to the window - we wouldn't notice it, but the birds would see a barrier. (I think it was when I was looking at window tinting solutions.. uv ray blocking).
If breaking up the reflection is the solution then I think sun catchers and crystals would be the most attractive options. Maybe when they've been up a few days you won't find them as distracting?
I like this idea: "Place thick planter boxes with flowers and shrubbery at the base of dangerous windows. This will encourage birds to land in the plants for shelter rather than seek escape through the window." but perhaps they would get in your way since your problem is with doors.
I hope you find something that works both for you and the birds.
9 Ways to Help Birds Avoid Window Collisions
Prevent Bird Window Collisions