Easy answer, there is no "claiming" the last 30 days of your Non-O , you would have to leave and re-enter the country to activate the visa, it can't be done in country. So easiest is the 30 day extension to your 60 day visa exempt.
Only the IO that you face can tell you that. Make sure you have the big 3 when you come, onward travel, 20k cash and confirmed accommodation, that is all you can do. Or buy a tourist visa before you come.
If you are never going to come back and need another extension of stay, then fine, just leave. However, to be on the safe side, you should do it correctly and cancel your work permit and then extension.