Ask your boss, has out contractor agreement been lodged with state government? If they say no, ask them why not?
I understand your concern, and have been in the same situation myself. And I understand you not wanting to kick up a fuss and risk a bad reference.
Everyone has posted pretty good advice on here. But you
can do something about it especially if you are an contractor working as an employee. Futhermore they will be fined by the ATO for not providing you with super etc if the decision is in your favour.
In regard to putting a claim in, keep your cool, man it out and start looking for a new job. Documentation is important, try keep emails and anything else relevant. I.e 'We have a flight at 10am, you are expected to report for work at this time' or whatever. To get back pay, holiday pay, super you don't need to file it on the spot. You could wait a few years and file it then. This saves you leaving with a possible bad reference.
Also if AFAP are telling you they can't help, that is garbage. Try LHMU or another union, they will get on their case. There are recent examples of people getting backpay from employers not paying the correct award.
Also while you are a contractor that makes you a sole trader. You can capitalise on this big time, talk to your accountant.
At the end of the day not paying correct wages and offering you a sham arrangement is nothing more than
petty theft.