Can I extend my visa at Chumphon immigration instead of Bangkok?

You can extend you stay based off your visa exemption (same as those with regular tourist visa) at every immigration office of your choosing. However, check into some accommodation (in the same district as the immigration office you choose) a night before and make sure they do the TM.30 reporting. You need to have proof of that (screenshot or paper receipt) - as some immigration offices require it even for a regular extension.