After some serious sleuthing (brown caterpillars are extraordinarily difficult to identify), we discovered we were harboring the youthful precursor of the pink spotted hawkmoth. The only way we were able to identify the darlings was by way of their dietary preference: Morning Glories. The Pink Spotted Hawkmoth is an enormous moth that is frequently mistaken for a hummingbird because of its darting vertical and lateral movements.
By an odd twist of luck, a few days later we happened to see one, AND I actually had my camera in my purse and was able to get some decent pictures. Additionally, I accidentally had my camera on video for a few seconds, so I actually got a quick shot of what their flying looks like. Enjoy!