Please do not misunderstand what I will post below. This is not to chastise you.
But it appears you are hanging everything on a technicality (just barely meeting the minimum presence obligation), one that depends on IRCC accepting your accounting of the facts, but overlooking other potentially negative factors and in particular ignoring the impact of being in breach of the PR Residency Obligation for nearly three years now, still being in breach, continuing to be in breach until the end of October.
It could happen, possibly, that IRCC will promptly, routinely issue a new PR card just three or four months after you have been in breach of the PR RO for over three years. Perhaps even give the application urgent processing. It is possible. You give IRCC information asserting compliance with the PR RO, throw in some supporting evidence, and IRCC accepts it without questions or non-routine processing. That could happen.
There is a big risk that is not how it will go. I cannot quantify the risks. I am guessing, though, in your situation a PRC application in January has a rather high risk, a very high risk of non-routine processing. Frankly, it would be crazy to expect IRCC to routinely accept your account of the facts and routinely issue a new PR card, let alone expecting urgent processing for a new PR card, applying just two months after being in breach of the PR RO for over three years.
I do not always connect posts in one topic from the same individual in another topic. But I vaguely remembered responding to some other query you made in another topic.
While there are undoubtedly many other particular facts and circumstances which loom large in your situation, the following illuminate enough to put a January 2018 PRC application into perspective:
You are not merely
cutting-it-close. You are currently in breach of the PR Residency Obligation. You have been in breach of the PR RO since at least September 2014 (once you were outside of Canada for 1095 days after you landed). You will continue to be in breach of the PR RO until the end of October.
You have been outside Canada well over two-thirds of the time since you became a PR. That does not exactly show a record of settling in Canada to live here permanently.
You appear to confuse the extremely lenient minimum PR Residency Obligation, which is intended to facilitate a broad, broad range of contingencies and emergencies in life, as if meeting that bare minimum is consistent with the purpose of Canada granting PR status. Reminder: the purpose of granting PR status is so the individual can settle and live permanently in Canada.
No one at IRCC has access to a crystal ball. There is no absolute-truth record where a processing agent can just look into the file and confirm how many days a PR has been in Canada, how many days outside Canada.
"
It's not what you know, it's what you can prove." To quote a Denzel Washington character in a cop movie, which can be all too close to how it works if and when what the facts are is challenged.
Just
cutting-it-close invites a challenge. You have, in contrast, clearly been in breach of the PR RO for years.
If a reasonable person has cause to doubt an individual's account about where he or she has been during the last five years, but knows where that person was
most of the time, it is reasonable to infer that person was there, where he or she was most of the time, unless there is direct proof otherwise.
Were you inside Canada or outside Canada
most of the time during the last five years. Clue: two years is less than half of five years.
Again, Canada grants PR status so that an individual can settle and live
permanently in Canada. That's the purpose for granting PR. When a PR lives outside Canada more than the PR is inside Canada, contrary to the purpose for which PR status was granted, that is
obviously going to raise questions if not overt concerns.
Odds are not good that you will be able to obtain a new PR card in time to travel abroad in February.
Regarding obtaining a PR Travel Document:
I am really sorry about the situation with your grandmother, but if you leave Canada without a valid PR card there is at least a very substantial risk your return to Canada could be delayed. The PR Travel Document could take significantly longer to process than three weeks. There is a risk the PR TD application could be denied and you would need to appeal. Then, attendant making an appeal, you would need to make another application for a special PR TD to return to Canada pending the appeal. All of that could take a significant amount of time, during which you would not be able to return to Canada, until you obtained the PR TD, or had status to travel via the U.S. and could use private transportation to cross a land border into Canada.
That is, depending on just what proof you will have to submit with a PR TD application, there are some significant risks it could be difficult to get a PR TD.
How great that risk is might depend on how strong your proof is of having worked in Canada for two years prior to going abroad. Pay stubs and T4s from a readily recognized Canadian business, that would improve your odds of the PR TD being processed more or less routinely. In contrast, having pay stubs from a small, low-profile employer, or especially from a sole proprietor or family member or friend, could make proving the case a little more difficult.
Part of the problem is that if you are abroad without a valid PR card, you are presumed to not have valid PR status.
Technically the statute states:
". . . a person who is outside Canada and who does not present a status document indicating permanent resident status is presumed not to have permanent resident status."
See IRPA Section 31(2)(b) at
http://laws-lois.justice.gc.ca/eng/acts/I-2.5/page-8.html#docCont
The "status document" is a reference to a PR card.
That is a rebuttable presumption, and for most PRs readily, even easily rebutted. And actually that is what the PR TD application process is about, the PR submitting sufficient proof of PR status and compliance with the PR RO, so that the visa office will issue a PR TD.
But your history is almost certain to invite not just a more thorough review, but a more
skeptical approach.
But there are many other aspects to your situation which may have significant influence. Those could have either positive or negative influence depending on what they are.
One circumstance which may be relevant is how things went at the PoE when you returned to Canada in October 2015. You were already in breach of the PR RO then, by over a year. How and why you were not reported on that occasion could be a relevant factor. And again, that could be either negative or positive.
Overall, however, the odds appear high that traveling abroad early next year will have substantial risks.
