Hi Lbr272,
As suzimac says just make sure you request they put the note with flight date (maybe give yourself a couple of days additional travel time) on your file. This worked for me last week. I spoke to someone late Thursday and it was approved Saturday morning and I received the passport Tuesday morning. Please note they don’t update the system that often so I wasn’t expecting my passport. It arrived before they sent the email message to say it had been posted.
I do think they have to quote the 10 weeks but they do seem to respond if your travel is imminent and you let them know.