After the last immigration crackdown immigration themselves said
that they would allow teachers to work and would not punish schools once they were taking reasonable steps to acquire the correct documentation for their teachers. This is 'Thai Visa Advice' not 'Thai Legal Advice' and that's how they do visas here, it's their law they decide how they want to enforce it..
Sorry David, this is not my personal experience I arrived on a tourist visa and has it changed to a non-b in Chaengwattana, I've never had to leave Thailand for anything visa related but I have friends working for international companies who got there their visa before coming to Thailand.
2 copies of all your documents, passport, degree, transcripts, maybe a copy of police clearance (I've never needed to provide one), contract from the school. My school (government) also sends signed copies of my directors Id card and other school documents (all in Thai so I don't know what they are) along with the application and acknowledgment of overstay rules
To get your non-b before you arrive?? No, it's not impossible at all, applying for a non-b in your home country is no different to getting it in Vientiane, once you have all the paperwork
Unless it's an agency placing you in a international school there is a 99% chance you are being led on, I have never heard of any agency in the government/ private circuit providing a visa or work permit before you've started working.. you can work here while your visa and work permit is being processed, it is technically illegal but so is riding a motorcycle without a helmet