Take your work permit into the labour office with the cancellation of contract from the employer, you will be given a pink letter confirming no outstanding tax. Next take the letter and go to the immigration and cancel your Non-B. ( I think same day you can apply for another visa.)
Update Bangkok immigration office: If you have an Non- B visa in order to change it to your new passport you will need a photocopy of your work permit ( vaild date ) Its not on the list of requirements but you will need it.
If they are clueless as you say , just go to your local immigration and ask what documents needed to extend. Be polite and wai and they might give you the answers. Good luck!
Not sure , I read a comment from an employment agency. Saying "they can't process the documents" , maybe something to do with the police clearance who knows?