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.
That's false. You can convert a visa exemption stamp to an ED visa inside the country. Whether or not the school will have the time to prepare the ED visa documents in time depends on the speed of the school.
And avoid any school that asks for "visa processing fees" or "visa renewal fees." This is a scam practice that some bad schools do. A visa costs 1,900฿ at immigration to get the ED visa, and 1,900฿ to renew your visa every 3 months. Nothing more.