Don't be shy about handing Alice to Jason and saying, "Could you take her for a bit? I need to sleep." Even if Alice gets a little hungry in the mean time, he can walk her around or swing her or something, and you can sleep. It isn't going to kill her to wait a bit longer to feed, and when she gets REALLY fussy, he can bring her back. Having at least one decent 2 or 3 hour sleep period can be key.