Well in hindsight you could have applied to renew your card back in June and by now you could possibly have received a new one.
You can apply for a PRTD from outside Canada even if you have a card that is still valid. People do this all the time where they travel and forgot to take their card with them.
There are no published times for PRTDs and not even worth speculating how long they may take as can even vary depending where or in which country someone applies.
Given card renewal processing is quoted as 90 days currently seems your only option might be to cross into the US via a land border and fly internally in the US out and back. Or fly out from Canada to the US and return via the US/Canada land border.
Interesting though that someone maybe forgot to tell immigration that the Vacs in NY and LA were closing permenantly
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