Feel your pain!! N Georgia mountains have a gabillion lady bugs every late fall. They gravitate to anything that protects them from cold and wind. They also get in through the smallest of openings. We NEVER CRUSH THEM. The fluid stains. We keep a charged, cordless hand vacuum within reach and suck them suckers up and go and dump them out daily. We even place tape over the suction area so the do not crawl out!!
This too is an annual inconvenience.
I tried "talking nicely" to them. DID NOT WORK!!
Perhaps someone has a better plan for both your moths and my ladybugs!
And NO, damned things are NOT CUTE!