Not quite sure what your circumstances are, or what you're after. If you're looking to get on to the card promoted in this thread and you're an existing card holder with ANZ, just pay the existing one off. Apply for this new one and away you go with your 16k bonus and no annual fee.
If you're looking at balance transfer stuff I suppose it gets a little more complicated, that's where I was lost in your post. If they won't waive the annual fee on your existing standard FF card then apply for this new one. Then after you've got the new cards ring up to cancel the existing one and they'll likely offer you to consolidate the two, essentially giving you a balance transfer and pro-rata refund on annual fee.
Generally I find ANZ to be frustrating to deal with on the phone. Most people I've spoken to seem to want to get rid of you asap. But, if you're persistent and reasonable you'll get what you need. GL.