I've never put mine on a windowsill, nor upside down - I wipe them off with a very dilute bleach solution (like, a splash of bleach in a bucket of water), dry them, and set them on the shelves that I use for starting seedlings in the spring.
In my experience, cooking them soon after picking results in a very watery puree. Even after curing for a while my puree has been much more watery than the "canned pumpkin" from the store; I've been thinking about putting it in my dehydrator for a while to take some of the water out. (Of note, I usually use hubbard-type squash rather than actual pumpkins.)
