Thanks for the input! Per your last paragraph ("Only wrinkle..."), do we even want to bother mentioning anything to the Canadian border officials about the Permanent Residency Application? Or just go into Canada like we might if visiting family (which I guess means it's a temporary visa). Or do I need to present as "moving" as you say, and she is just "helping"?
We are about to mail in our permanent residency application and spousal sponsorship application. And we want to move in four months to Canada. So we are just trying to predict how this move should be conducted if we don't have approval of our applications by then. I see no reason why they will not be approved. I have a job in Canada, am a US+CAD citizen, etc, etc so I cannot imagine any reason for rejection if everything is squeaky clean.
If you have already applied when you cross the border, definitely do not deny that there is the PR application in process. Doesn't mean you have to volunteer that, but do not lie.
It's not an obvious thing at border: they may not care, they are likely to be far more interested in self-isolation plans in accordance with law, or they may show some interest.
About the most one can say is that if your spouse is clearly moving - UHaul with all worldly possessions - it might seem rather obvious (unless credible to say the possessions are all yours and helping you to settle in). And it's fine of course if the spouse is staying for a lengthy period of time (typically six months given at border), and may consider applying to extend/staying if/when the PR application is approved.
Best I can suggest is to reply in as calm and simple a manner as possible, "I'll return to the USA when needed and won't overstay." Obviously if the spouse has a plan to return to USA for any reason in the coming six months or so, mention that (even if it's a short-term trip back eg to visit family).
I think the reality is that they're not overly concerned about US citizens with Canadian spouses. But it's still not a guarantee. Just note, due to covid, files are moving slower than before and there's a backlog. Still seems USA applicants are getting approved relatively quickly, but that still may not be quick.
(BTW once in Canada you both should update addresses with IRCC. IRCC wont' care if he's in country 'temporarily but for a lengthy stay.' For you will likely help file - approval of you as sponsor - that you've already returned. From what I've seen applications where sponsor-Cdn citizen is abroad usually have a note that the examining officer of the PA should also check the plans to return; it's not clear to me how seriously they do this but you fulfilling plan and taking job/moving at least removes that question.)