It takes a pretty hefty coating of casual grunge to block the mirror effect, depending on the angle at which the sun strikes your windows. That amount of airborne crud would probably obviate your need for drapes .
When I said “paint” you can also loosely interpret that to “smear”. You don’t need to actually employ a paint brush, just a sponge or soft rag. Be sure to use sufficient powder to make a goop that is substantial enough to prevent or diffuse that reflection, not just a light discoloration on the windows. The effect you want to achieve is frosted white window glass.
Oh, and you may find that the bird actually ‘fights’ at window sill level, where he can stand and attack his reflection best. So it may only be necessary to white out the lower portion of the window(s).
I am not aware of any systematic regional variation in female beak color. Although females have somewhat more orange bills than males, as I said to my eyes the color is generally rather more red than orange. All major bird field guides use “red” in the description of the female’s bill color but not all say “orange”: Sibley “red-orange,” National Geographic “reddish” (both sexes), Peterson “red,” Stokes “orangish red.” The Cornell Laboratory of Ornithology says “bright red bill.” A Google image search on “female cardinal” will also show many females with quite bright red bills. Maybe the birds in your area have a carotenoid deficiency.
Does it attack your windows all year round or just in fall and early winter?
We had a crabapple tree in our back yard, and birds would eat the dropped apples, which were fermenting, and then attack the windows. The kind of bird isn’t the issue, it’s the blood alcohol level…
In glut years for wild grapes, we get drunken grouse and turkey. It’s surprising how intimidating a bald headed, dangly-necked, clumsy bird can be when hopped up on juice. Couple months ago one hammered hen picked a fight with a garden rake. She won (I think) but her victory strut led her smack into the side of the shed.
A wild turkey sober can be intimidating as hell, there’s a reason old Ben thought they should be the national bird. Domesticated turkeys in a large group, because they’re dumb as anything, can also be a handful. But loaded? I can’t imagine.
I think of the following, the opening of the Nabakov masterpiece Pale Fire, whenever I notice or read about the phenomenon:
CANTO 1
I was the shadow of the waxwing slain
By the false azure in the windowpane
I was the smudge of ashen fluff–and I
Lived on, flew on, in the reflected sky,
We actually see quite a few bundles of ashen fluff who in full flight have misperceived an azure sky and hit that windowpane rather too hard for mortal tissue, but slightly before their shade flies off into the reflected sky. Sad to be unwilling participants in their crossing over. Others that hit with somewhat less velocity are amenable to medical intervention.
But the ones who become pugilistic with their own reflections rarely sustain significant damage. Their glass opponents seem incapable of inflicting injury. Funny how that happens.
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BTW, I wasn’t being sarcastic, I just wasn’t sure if it appears for everyone.