This is one of the rare occasions where it is okay to contact the search committee.
I would also recommend going to your university's graduate school or registrar and getting an administrator there to write a statement on university letterhead stating that you have defended and that the degree is expected to be conferred on Date X. Make a PDF of this letter so you can include it with any other transcripts you send out for other positions.
The time between my dissertation defense and receiving my official transcript showing that I had the doctorate was about three months. Three months is a long time to go with a transcript that shows you are still a student. So get that official documentation and submit it along with your other documents when applying for future positions.
Oh, and congratulations!
This is a great idea! I have two PhD students graduating this spring (after years of having none) so this is going to be very useful to them. Even if they defend in March, it takes a while for everything to show up on the transcript, and we're right in the midst of job search season.