Hi
I understand your concern and we also found the process very frustrating.
Just to correct you, it didn’t work out for us, as we missed our holiday due to my daughter’s passport not arriving in time.
I would say, based on our experience, if you haven’t received an “approved” message by 2nd Sept, then it’s unlikely you’ll make it. It then takes 2-3 days for the passport to be printed and couriered – TNT are the couriers and I’ve read different reports about them from being fast to being slow.
I did a lot of Tweeting and rang at least 10 times- just be a nuisance.
Also I was told by the PO that chid renewals (our case) don’t take as long as adult renewals, so perhaps that’s it?
Good luck.