I'm not aware of any way to ask for urgent processing. If you are currently living in Canada and you have an actual urgent need to go abroad, you can try to call IRCC and ask if there is a way the process can be expedited as you need your passport for a valid reason.
Even if you don't live in Canada, you can probably try to contact them by email. In the PPR email, they specify an email address you can use to contact them in case of issues.