Probably still unlikely. A whole bunch of effort for almost nothing, when you could simply go out of the country for a day or two. Don't know why you so much insist on avoiding a short trip, and create a whole bunch of challenges and work for people. Might not even work in the end.
It's theoretically possible to get an "extension based on working," but highly highly unlikely you will be able to. You might also get the extension, but have issues with the work permit since you have an ED visa. I was in the same situation, and so was another teacher I know. In the end, it was simpler to go out the country and get a Non-Immigrant B visa.
Sorry, I don't know how Bangkok schools work as of right now, or all other provinces. OP didn't say where she will be living. I know where I live it's possible.
That's very strange. Would be interested in a source on this. ED visas are still being offered. I contacted my private school and a university just two weeks ago.