The best solution would be if you took a 2-3 day trip to Malaysia or someplace similar. That way you get 120 days total in Thailand and you get to visit another country.
Think of it in the simplest form possible, just as Thai immigration does. Put your home country as residence and tourism as reason. It's called "Workcation", which is a form of vacation.
There is no time limit for staying outside of the country. If you get let back in depends on the immigration officer at the border and your travel history.