Talk drywall to me

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Talk drywall to me.

No, seriously. My parents had a hardware store when I was a kid, so I'm pretty decent at simple home repair/improvement stuff, but I need a bit of help here. If anyone reading this is handy with these types of things, you'll have my eternal gratitude.

Say you're trying to find some way to put an interior shade mount on a drywall-covered window well, but you can't use regular anchor screws because when you start drilling you only get three quarters of an inch in before you hit something really freakin' hard underneath that's impossible to drill into. The only thing I can think of trying is maybe I could get some reeeeally short anchor screws, but do they even make them that short? Or what else should I look for tomorrow morning when the hardware store opens?

It's just a cellular shade, so it's pretty light. And yes, I've already considered mounting the bracket externally, but whatever the heck it is under the surface all around my window is there too.

I'd call some of my guy friends but they're all city boys who have no clue how to do this. I'm the handiest person in my social circle. Google's not helping much so far. So, handy people of Brooklynian, can you help a neighbor out here?

Otherwise, I'm just going to end up duct-taping that mofo up there, and that would really clash with my silk sheer drapes.