Wow Jen! It's the first time I've read this thread and WOW you've been having a rough go.
I worked in 2 of the Big 4 banks for years before I became a mortgage broker (including ANZ) and I think your bank manager has been acting shamefully. And frankly, I'm furious on your behalf.
At this point, my best advice is that you don't talk to your Heidelberg manager any longer. She doesn't have the authority to sort this out for you, and she apparently is more interested in covering her mistakes than in actually doing the best thing for you.
The first port of call is her immediate supervisor. If they stonewall you, or don't sort the situation out, then ask to speak to the area manager (or next manager up). Usually, by one or two managers up the line, you will get someone who percieves the bigger picture (ie not just protecting the branch managers ***) and most importantly, to a manager who has the authority and the willingness to sort it out, rather than face the potential PR nightmare.
I do think that the bank cannot change the terms of a contract that has been signed and settled already, unless the loan payments are not being met, but I'm a layman, not a solicitor so don't take that as gospel.
From your recent posts I'm getting the impression that you'd rather just let sleeping dogs lie, and if they stop hassling you, then by all means do.
If they bring it up again, I do suggest that you tell them you're going to approach the banking ombudsmen about the matter, and I suspect that will be a very good motivator for them to resolve it to your satisfaction. If it's still not resolved (and by that I really mean that you get to keep the excellent existing contract without having to pay any fees including the extra LMI) then do go to the banking ombudsmen. Don't let them disadvantage you by pushing you until you either except their less advantagous deal, or you refinance elsewhere. Neither of those options is in your best interests at all.
But mostly... Good Luck! and do keep us updated!