Offered sale prices for RVs do not usually include taxes and fees (those will be added on during the sale). Price differences for the same TT may partly reflect options, will mostly reflect what the dealer thinks he can ask in the local market. You will find variations in price among dealers in a single state.
Price differences for a "similar" TT might reflect that the models for which you are comparing prices are not so similar as you might think. Different manufacturers build TTs differently: structure, materials, build quality, so have different costs and different prices. Even within a single manufacturer, different model lines offering similar floor plans will reflect quality and cost differences, 50% to 100% not unusual.
People who live in states with high sales taxes will try to buy and register a RV in a state that doesn't have sales taxes (Montana is a popular "no sales tax" state). People who live in states with high registration fees or annual property taxes will try to register vehicles in states without those taxes. The usual mechanism in both cases is to set up a legal entity in the low tax state to own the vehicle, which gets leased back to an individual who resides elsewhere.
South Dakota is different. South Dakota is popular with full-time RVers who are trying to avoid paying state income taxes, and so domicile themselves in South Dakota, which does not have such a tax. South Dakota is more popular for this than some other no income tax states is because its laws enable domicile for people who are not physically resident, registration fees and vehicle taxes are reasonably low, license renewal and absentee voting are made easy, and it is possible to get medical insurance that covers one outside the state. But the easy legal climate also works in favor of solving vehicle registration problems for non-resident aliens.
If we live in one state and want to purchase vehicles in another, how easy or difficult, and what are the added expenses, depends on the tax laws of each state and the reciprocal arrangements between the pair of states. Cross border vehicle purchases, to register in your home state, are usually easy. But some people live in one state, purchase in another to avoid a sales tax, and register outside their state of residence. Some people get caught by the state they live in, end up paying penalties in addition to the taxes.
But as a non-resident, this should not matter for you. I suggest you think more about who, in what state, can make your plan possible, rather than trying to pin down the lowest purchase price or the lowest taxes and/or registration fees.
An agency in South Dakota or Montana would be the most likely place to start, because the state tax driven market for these services points to those two states, depending on which tax the client is trying to avoid.
Coming from Australia, your port of entry is probably California. While California might be one of the worst places for cost and red tape, even in California there are agencies that work out things like this for non-resident clients. Because of the amount of ex-pat traffic back and forth in the petroleum business, there is likely a legal firm or agent in Perth that has connections with an agent in LA or Houston that takes care of acquiring and registering vehicles for visitors, although my experience is that most cases are handled by leasing.