@AlPage48: "For the marriage certificate authentication we're out of luck"

It's not just you out luck, it's same for all nationals. The initial info from PSB about the authentication was wrong or misunderstood.

Authenticating foreign documents to be used in China is a multi-step process in which a foreign consulate in China has no role.

Their boss, I assume in case of USA the Department of State and related office in USA, however has a role. They need to authenticate a document before it can be authenticated by Chinese consulate in USA.

For documents to be used in China, the final stop is always the Chinese consulate in the country where the document originates from.

Similarly if you want a Chinese document to be legit in USA, the final step is US consulate in China.

That said, some consulates or other service providers may provide service where they will send the relevant document abroad for said processing. I don't know any that do, and at this particular time courier options may be even more limited.

Going a bit off-topic, but anyway.

@AlPage48:

"if I can get our American issued marriage certificate authenticated by the American consulate then they'll give me a 1 year residence permit

[...]

although we were married in America, we are Canadian"

If both of you are Canadian like you say, and neither has Chinese nationality, then I doubt that you can get 1 year RP - or does your Canadian spouse already have valid residence permit here, and the visa hassle is only yours?

Or if there is some dual nationality thing going here, it could land your spouse in trouble with that.

Problem for Entry & Exit now is, as OP well described, that there are some fights available. They are not qualified to judge whether some random foreigner qualifies to the "essential to travel" group or not, so they have to leave that burden of proof to the individuals. It was easier when there were simply no flights available at all.

If there are some flights available (to your home country I guess), I would think that you need to confirm with the relevant airline(s) whether your situation equals "essential" need to leave China.

For example my national airline company has chat service on their webpage, and if I was in your situation I would screenshot a statement in their support chat - them saying that sorry, you are not eligible to fly on our flights that are reserved for essential travel.

Or if they say sure you can board us and the ticket is 1 million euros, then show that to Entry & Exit, along with your bank account statement showing lack of such funds.

I get the platform's launch page:

"222222222222222222222

If you see this page, the OpenResty web platform is successfully installed and working. Further configuration is required."

Maybe you are using some other URL than just "en.kunming.cn" ?

My own anti-foreigner sentiment is growing lately.

In past I have posted some sensitive content on this website (on personal level anyway, since it deals with genitals of my own and of family members), but I don't seem to find a way to self-sensor it out myself. Kindly asking for assistance.