Aussies starting USA company
First of all congratulations on growing your business. As far as establishing a more solid presence in the US I would say it's a business decision that you will need to make yourself. On our end I can tell you about the technicalities of each of the scenarios you consider for this expansion.
Technically you can continue doing business using your Australian company, however, as you already understand correctly, it is much easier to do business in the US using a "local" US entity. Once established, such entity will enter into formal business relationship with your Australian entity, or if you like you can just use it as primary entity for your business (a US company can have primary business address in Australia).
Any one of those scenarios allows you to collect payments through PayPal, transfer them to US bank account, and then transfer them to Australian bank. The accounting part of those movements will need to be verified with your accountant, but in general there is nothing unusual about that plan.
To open a bank account you will need to travel to the US at least once, but after that most banks will allow you to control most of the aspects of bank account management online or by phone. I would recommend opening Checking and Savings account together (just in case).
I hope I answered most of your questions, but if you are welcome to ask more.