We have a similar annual issue with swallows, but nesting outside over doorways (plop! on arrival and departure). If we can knock down the nests before they lay to encourage them to lay elsewhere (there are good places on the property), we do, but once they lay and sit, they're in for the duration and so are we. They repay us by eating up most of the skeeters that would love to come in those same doors-- if we open them at night.
Your guests are probably forestalling rabid bats, so you're ahead of the game.
You could consider dumping porta-potti liquid enzymes into the "stash" to neutralize the organic matter. Unscented of course.