Its late, so I'll keep it short for now.
1. There are two places you could keep a journal of your experiences: either here in this very Antibiotics forum or in the Regimens forum, or start a blog on CPn Help. Or do both, as I and several other people do.
2. There is absolutely no reason why you should not take both Copaxone and antibiotics because there is no interaction.
3. There are several people who are following either David's treatment or the original Vanderbilt one who live in Australia, in fact it seems to me that Australian GPs are more open-minded than many others in the US and UK. Your neuro might be more difficult to persuade. If you think this might be the case yet your GP is willing to prescribe, do it through your GP. My neuro when asked to have a look at my new MRI by the radiologist, just said: "I can't see that!" and wouldn't even look. He does seem to be more warming to the thing, though. The person who has been the longest on the regime to my knowledge in Australia is CureOrBust. He writes on both sites, so you could send him a private message asking him for some advice. He lives in Sydney.
As far as persuasive material, this pdf file from David's site is a very good thing to show doctors, without overburdening them:
It is only about eight pages so they have more chance of taking it all in.
Best of luck,