About the magic chop.  My first full scale kid swarm had second graders shoving notebooks and pens at me wanting autographs.  Of course, the pens were point first, so not only did I get jabbed, but I also had ink marks all over my arms.

So, I arranged to get a self-inking chop made with my name (in English and Chinese) and a short line in Chinese telling them to study hard.

Every time I remembered to have it with me, NO ONE wanted an autograph.  But, when I didn't have it with me, I'd get at least one swarm coming in for autographs.

In Xiangtan, I forgot it on day 1, so had to sign by hand the first evening.  I put it in my pocket the next day.  Several autograph-free swarms happened and finally on the last day, I got to use the chop with some high school students.

So, for good or bad, the magic chop that prevents children from wanting autographs has lost its ability (or was just overrun by so many students).

I think you can just buy them online. They don't check that hard
I would really really recommend a CELTA because it just makes you better at teaching and is lot of fun to do, but for visa purposes you can get a shady one pretty cheap

I found this brilliant VPN called Wallless for 20rmb a month that works on my android phone and PC.
That is the price paying by the month which I am doing because I imagine that it will end at some point.

I believe that the visa requirements are just that you have a Bachelor's degree and a teaching credential and the rest is up to the discretion of the school.

Some classes have more than just "possess a teaching license" or "have a TFL certificate" as a requirement to be an instructor.

One thing you could try.  If California lets anyone, regarless of status, take a teacher certification exam, take those for the specific subjects.  Or, fly to Florida and take the tests.  In Florida, you need a general teaching cert and also to pass a test on your specialty.  The trick is that you can take that specialty test any time you like, even if you don't currently have a teaching cert.  Maybe California works like this, maybe not.  They have tests for so many things, including school admins as well as guidance counsellors.  They also have separate tests for Junior High and High School level of many subjects.  Visit the state Dept of Education website for California (and maybe Florida) if you want a full menu of available exams.  In Florida, these can be taken online at a number of testing centers around the state, so there's now worry about having to wait months for a test date.  I have no clue how California has them, but their Dept of Edu site should lay it out simply enough.

In China, being an existing acknowledged teacher, plus showing them that you've passed the subject-specific certification test from a US state might (or might not) be enough to meet the Chinese standards, so you should probably ask "Hey, if I've got a passing score on the cert testing for teaching this from the US, will that and my current qualifications be enough?" before you leap on an airplane.

If you can get them to agree that this makes you a subject matter expert, that's the time to look into a visa/RP change.