Sorry, but you are wrong. What you are calling a visa, is actually an extension. Extensions are cancelled, visas are not. This is why mods check posts, so that incorrect information is not passed on.
99% of YOUR employer's maybe, but that is most certainly not the norm. Also, I have never had an employer ask to keep MY work permit, so again, you are just talking about your experience.
You are pretty well spot on, BUT the work permit belongs to the employee, NOT the employer, and it is the employees responsibility to ensure it is cancelled
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.