I don't want to be disingenuous in my application by promising the world premiere to everyone, but not having had it yet, see it as a sweetener for the cover letter. Should I hustle it until I have it?
You definitely want to use your premiere status to your own advantage, but be honest about it and clearly communicate all changes to that status. You might be tempted to refrain from notifying the other festivals, but that will only create an awkwardness if and when that other festival calls to notify you of your acceptance.
The following sentences added to your submission's cover letter will cover most situations:
As of this writing, the world premiere of "Example Movie" is still available. We have submissions out to several festivals and will keep you apprised of any premiere status changes.
When you decide to have your world premiere at a particular festival, simply send an email to the other festivals still considering you with the subject line "premiere status update for EXAMPLE MOVIE" and let them know about your film's upcoming screening(s).