I'm not sure how long passport renewals take now, but when I did mine, it took 5-6 weeks, so was able to make the 3 months required by UKVI to replace the BRP. I do hope you get yours sorted quickly.

Anyway, I'm not sure which form you need to use. This link https://www.gov.uk/change-circumstan...and-have-a-brp states which form you need to use although in that form, there's only options for PBS migrants. It's probably best for you to contact UKVI through phone so they can guide you accordingly. They've done a lot of changes in forms and what they do know is make it more difficult and complicated.