Except a tourist visa to a Non-Immigrant Type visa you CANNOT switch from one type to another. :/
As
@Da***
, (y) correctly pointed out you can go from an extension based on education to an extension for another reason.
You take paperwork from your school AND paperwork from your company (along with proof you've applied for a work permit) and go to the immigration office.
You would cancel your extension based on education and immediately apply for a new extension based on employment. It takes some coordination and making sure all your documentation is correct, BUT it can be done.
Keep in mind you can't hold a work permit or legally work on your ED visa.
Perhaps it's just as easy to go get the 90 day single entry Non-B visa from a thai consulate like your employer is saying.