In 2016 we registered our American coach through a Limited Liability Company scheme in Montana (zero sales tax) and were in the US on a 10 year visa which allows 6 months in any year. Insurance was expensive as we did not have a US driver's licence and not many companies will insure on a UK licence. After a year the insurance broker did get the insurance company (Progressive) to accept our UK driving record which you can printout from DVLA. Back in 2002, we registered a coach in South Dakota (paid sales tax) and had an address at a mail forwarding company in Sioux Falls and took the US drivers test, only problem there is the licence is only valid for the period you are in the US, so 6 months.
Since my first posting, I have found progressive to be very good to deal with and have now used them to insure our RV. We also own our vehicle through a LLC based in Montana. As it’s over 10 years old a one off lifetime vehicle tax also applies. We are off on our maiden road trip in a couple of weeks, Arizona, Southern California, etc.