Good to hear you've got the diploma. I'm currently working on my diploma and will be looking at OJT after that.
Did AA issue you with the OJT book? If so, can it be used to record work performed on any aircraft, whether type-rated or not? As this is something I'm trying to find out about OJT books.
Tiger tend to have 2-3 aircraft on the ground overnight in Sydney each night. As an AME, I would guess you'll likely be on permanent night shift, but you will get some decent OJT jobs. A lot of overnight servicing is pretty routine: oils, cabin stuff, wheels & brakes, etc. but every now and then other things pop up.
Of course, if relocation is a possibility, try BAE in Melbourne where you can do overnight servicing on the tarmac as well as get the A checks in the hangar. I think they're still advertising.
Cheers,
John