Kit's doing well so far. She really began feeling those contractions this afternoon, in response to the Pitosin (synthetic hormone to induce labor). They're slacking off on that and providing her some painkiller in the hopes that she can get some sleep tonight and be rested for tomorrow, when we expect actual delivery to happen.
I'm at home for the night, also trying to get some sleep.
And special thanks to 3catsjackson, who actually got Kit to the hospital, got me from the airport to the hospital, and has generally been exceedingly super helpful.
Thank you all for the good wishes! I'll post more news when I can.