UPDATE!
I finally have both my passport and BRP! I withdrew my application but checked the option to carry on processing my application if it was going to be decided within 10 days, and had to send another request when my documents still hadn't arrived after 10 days. I finally got everything back yesterday morning.
Here's my timeline if it helps anyone else:
Type: BRP NTL (transfer ILR visa from an expired Canadian passport to BRP card)
Application sent: 02/02/2016
Application received: ?
Acknowledgement: None!
Biometrics letter received: 19/02/2016
Biometrics taken: 20/02/2016
Application withdrawal sent: 28/04/2016
Progress request sent: 12/05/2016
Documents and BRP received: 18/05/2016
So, it took 3 1/2 months in total with 10 days to spare before we fly on holiday. Phew!
What a horrible, stressful process!!!