@Jessie *****
I believe you're thinking of applying for a new Non-Imm visa inside the country, that requires a minimum of 15 days left on your passport stamp
BUT
all you're doing is changing the reason for your extension to one from SMART visa to one based on employment
Go to Cham Churi about a week before you're termination date for the smart visa paperwork, they should cancel the extension and give you a stamp that lets you stay until the termination date on the paperwork. You have until that stamp runs out to go apply for a NEW extension for a different reason OR leave the country.
I'd also go out to Chaengwattana and get the hand out listing the requirements to get this new yearly extension so you're not a document short when you try for it. You won't have the luxury of time on your side and it has to work pretty much the first time you try or you'll run out of time on your stamp