For the record the Thai consulate in Saigon will issue a single entry non B without needing proof of filing for a work permit. Last month I collected my second back to back non b there.
You used to be able to get a one year multi entry B visa without a work permit, then a few years ago they changed the rules and you can now only get a single entry non b if you don't have a work permit.
The embassy staff who took receipt of my second application was less laissez-faire and quizzed me about not having a work permit. She also insisted on seeing a flight out of Thailand which meant I had to buy one (which I probably won't use).
I'm guessing 2 non b is the limit. So my next visa will be a tourist visa from HK.
I applied recently (a month ago) for my second non b from Saigon. I had no WP3 (whatever that is). Just the invitation letter and all the regular company docs.
Companies (ie Not schools) should have no issue paying as they are likely paying you several hundred thousand a month. Teaching jobs on the other hand, especially if just some small local school paying low rates probably don't want the extra cost of visas.