To throw in my two cents... I am an American and I have had a lot of trouble understanding South Africans pronunciation. I don't think this is because they pronounce it incorrectly, but because I have never been exposed to the accent before. I can understand how it would be confusing to kids who are trying to learn a new language to have the 'rules' change every time they get a new teacher. If I am a fluent English speaker and I have trouble understanding some South African accents, I don't expect the students to be better at it. Some South Africans I have no problem with, but some I had to listen very closely and ask them to repeat things. Again, not their problem but mine. However, I can understand why a school would want to 'pick one and stick with it' instead of changing pronunciations. I'm not saying I agree with it, but just that I can understand it from their perspective and I could see why they would want to do it that way.
That being said, the school hires you knowing where you come from and what accent you have is part of the package. If they want an American accent taught, they should hire an American teacher. If they don't want the American accent taught, hire a non-American.
Also, our contracts basically say that we are here to do what the school asks us to, whatever that is, so I'd be careful about openly refusing to do something. (Do it the Korean way where you say 'yes I'll change my accent' but then don't. And if they inquire about it you say 'what?'
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Maybe you could even start with a lesson about pronunciation and how it's different between nations - highlight some of the key phrases your students have trouble with and practice letting them hear your pronunciation when they know what it means. I find it helps my students if I am really clear about what I expect them to do and know in class.
