I ended up calling in and waiting about 35 minutes on hold before getting a person. Exact flight that I wanted was sold out (even though I had it in my cart on the JB website before it went down!), but I was able to book one for the day earlier at the same price (3,800 True Blue points +$5.60). Not bad for a JFK -> LAX flight.

Looking at Twitter it seems like that's really the only way to get a flight booked right now unfortunately, and I'm sure the deals are going way quickly as more people are able to call in and book.

Not a super well executed sale, JetBlue.