Let me properly format my timeline:
April: entered Canada on TRV
August: received AOR and applied for WP immediately. AIP received after 2 weeks.
Dec: WP was refused becuz IRCC said I was out of status and not eligible to restore since I've lost my status more than 90 days.
You haven't stated when you applied for spousal sponsorship.
Now one small note: if you received AIP already, and assuming AOR was 30-60 days after you applied, there is a decent chance you'll get PR approved fairly soon, and before you would (at this point) have any chance of getting the work permit approved. And pursuing the work permit now energetically might (perversely) slow down the PR processing (if the officer involved has to deal with the paperwork about your work permit, and I don't have enough info about their internal processes to say). Caveat of course that I have no idea how long your PR might take at this point, either.
So you have some choices to make. Some things you COULD do:
-order gcms notes. Would take 30 days minimum, usually, possibly longer. At least it would not slow down your PR processing. You may be able to piece things together with that to figure out next steps.
-You could write to request reconsideration based on the facts that you lay out (I'd suggest without attacks or snark).
-You could apply now for restoration of status - again, laying out just the facts about when you entered and noting the info about your status expiring that was used to say you're not eligible was incorrect. (Avoid attacks or snark).
-Once that is done (assuming it is approved), apply for work permit.
Again, I do not know whether request for reconsideration/restoration of status applications would slow things down; I suspect they might.
Attacks and snark (as I noted): my experience is bureaucracies (and the individuals within) will react to attacks and threats, particularly legal threats. That doesn't mean one should never use them, but tactically, and only when it makes sense.