It's good to read something from someone who actually understands the situation on the ground re teaching in China. I've experienced the same things you have during my few years as a foreign teacher of English in China. I've also been teaching without an RP for a week or two in the past. There is nothing to worry about doing so. After all, if immigration gets involved, your employer will have much more to lose than you. So, he'll make sure that won't happen.
There's no substitute for experience, and those immersed in the Chinese education system at present have more up-to-date knowledge to impart than commentators far afield who give befuddled advice!