I believe you should receive your PR card before your trip if you do the Flagpole next week or the week after. The CIC timelines indicate 26 days and CBSA agent stated 6-8 weeks. Which any which way is before the end of February. So you should be covered.
I also found this link where you can request for urgent processing of pr card:
https://www.canada.ca/en/immigratio...rants/pr-card/apply-renew-replace/urgent.html
This may or may not apply to your scenario, but you can check it out.
Lastly, yes, go ahead and send out an email requesting for the interview. If you get it sooner, that's great! If not, you can fall back on Flagpole. Just ensure to set a deadline for how long you are willing to wait for the interview reply, and if you dont receive it by then, you'll Flagpole.
Do check the Flagpole timings as well to help with your plan.