I am currently working on a teaching project which is due to finish at the end of February. I have a non immigrant B visa and work permit. The visa visa is due to expire at the end of January, so I will be getting an extension for this.

When my project finishes I will be looking to start work at a different school.. Am I right in thinking that the day my project finishes I will have to leave the country to get a new visa.. And then when I find a new job, do another visa run for a non immigrant B visa and then get new my work permit?

Thank you for any advice you want to give.

Correct

Either leave or apply for a 7 day extension (1900 baht). You have to cancel your extension at immigration on the date your job ends by showing a letter from your employer.

Correct. Unless you find a job before the curent one ends.

You can get a an extra 7 days from immirgation in which to get a new work permit and apply for a new extension of stay based on working for the new employer.

You are correct and a tourist visa from a neighboring country would give you some time.