I’m in a very similar situation as you! Flying out a bit later but the rest is the same.
I’m even having doubts about getting mine on time, to the point I’ve lined up my mate that’ll replace me!
That being said, being on here won’t fill you with hope – you’ll likely only find people with horror story waiting times as they’ll be the ones asking questions – someone who got one on time won’t likely come on a forum to discuss it.
Ultimately, it’s a case of praying. The helpline is absolute no use as I’m sure you’re aware. I’ll keep my fingers crossed for you!
Again, similar to me – you can’t even fast track it as it is your first one which is a farce in and of itself. I’d maybe suggest contacting your MP if you’ve waited longer than your minimum time (10 weeks providing they keep the same waiting times nation wide)
Have you had your interview yet? I believe that’s a mandatory requirement for first UK Passport…
All the best!