@minesasangria my timeline in terms of application date vs flight date is pretty much identical to yours. I applied end of March, and I need my passport by the 23rd May.
What I ended up doing is:
1.) reporting my passport ‘lost’ (this is a risky and controversial move, i know, but it meant that I did not have to wait to get it back, which would have elongated an already very long withdrawal process)
2.) sending a withdrawal letter (I sent it on 7th April, first class)
3.) booking a fast track appointment (booked it for the 25/04, just had it this morning) and
4.) filling out an application form to replace my ‘lost’ passport to take to the appointment.
Now, I really got lucky because my appointment was today and they only just processed my withdrawal yesterday (they will send you away at the appointment, if you have got another live application). Considering the fact that I sent the withdrawal letter on the 7th and it was not officially withdrawn till the 24th ( and that was also with calling them twice to make the withdrawal urgent!), perhaps withdrawing and booking a fast track might not be the safest option if your flight is in less than 4 weeks, if we use my timeline as a reference.
I’ll say, hold out for the upgrade. I really hope you get your passport on time, sending all the good vibes your way.