I've lived with tinnitus for the past 15 years or so. It's never given me any problems with Oz or PNG medicals so I don't think you'll have much of a problem. I agree that it's best to get the first appointment of the day with the DAME, after a night of restful sleep in a very quiet location. Even so, as has already been pointed out, there's a chance that you'll miss one or two of the tones due to being at a similar frequency to "the bells", but I've always managed to get through the stage 1 test.
Judging from your post, the problem is just beginning for you. It'll take a bit of time to get accustomed to it but you'll find many times where you're not even aware of the problem. The first time you take the test, just close your eyes so that you can concentrate on the tones without any visual distractions.
Unless there's another (underlying) medical problem, I'm sure you'll ace the test.
