J.C.
These are all great suggestions. Don't feel shy to reach out in your neighborhood or community. I know as a mom, it's the sort of thing I would definitely be willing to help with. On the other hand, as a mom I know that sometimes other things get in the way or my kids might be sick, or we might be out of town. So you'd want to have 2 or 3 people lined up.
Another thought is that you might check with your OB or midwife practice to see if they have a name of a baby nurse or newborn sitter agency. You would pay top dollar, but you would get referrals to people who are used to working nights or weekends.