First off, thank you to all who read my dilemma and offered advice. I really appreciate it. :-)
The annulment process has officially begun. I already sent back the paper saying I don't object to any of the judges who will be working in my case. (I don't know any of them, and considering my ex is Jewish, I doubt he knows any of them either.)
I spoke to one of the secretaries for one of the priests (who is also the presiding judge) and she told me that Father said that my case is top priority over all of the other cases. They have also waived all fees. I told her that FI and I are doing the Pre Cana this Saturday and next Saturday. She said we should definitely do it. The only thing is that even though my case is first, there's still no guarantee that the annulment will be granted.
I'm cautiously optimistic, but at the same time I still feel like FI and I need to see about a backup Church and ceremony.