Can I cancel my work contract and apply for a new Non-B visa in Thailand?

Good afternoon all. I have a fairly simple enquiry. My background is as follows: South African teacher with a work permit and an extension of stay both valid until 1 May 2020 through a language school. My school will close for the year on the 29th of March, and I will then end my employment. I will take up employment with a new school for the coming school year. What I need to know is: if my current employer agrees to do it, could I go to Immigration before the end of March with a letter cancelling my contract on the 7th of April to give me a few days to pack and move before I have to leave the country to apply for a new non-b visa? Also, I haven't seen much from South Africans lately, but which Embassy close to Chiang Mai is still fairly friendly toward South Africans? I'm considering Vientiane or Savanakhet.