I decided to contact them on Twitter, and saw that they were replying to queries by the minute. I was very impressed! All I had to do was DM them my confirmation number, and they replied within 7 minutes giving me options and other dates with available flights. I have never experienced such prompt service in times like this.
I highly suggest contacting them via Twitter (@JetBlue) if you are flying with them.
Well done JetBlue! Other airlines, take heed.