... in 2007 I bought my RV in California and was advised (suggested) that I buy it out of state using an LLC.
Does that mean you purchased the RV in California and took delivery in another state? Or did you you purchase it in another state and take delivery there? In which state is the RV registered? Am I correct in assuming you didn't pay sales tax to California or any other state?
California's "out of state delivery" provisions allow you to buy in California and legally avoid paying sales tax in California. They require taking delivery in another state and keeping the vehicle outside of California for 91 consecutive days out of the first 6 months of ownership. They also require that you be able to show you bought the RV for use outside of California, which involves filing a form with the Board Of Equalization and having receipts that "prove" you used the RV outside California for 91 consecutive days, e.g. receipts for fuel and campgrounds. Storage fees do not count, although some folks use a campground for storage and claim they were "using" the RV there.
California may (often does) "audit" folks who take this route, meaning that they send out a letter asking for proof of the out of state delivery (this would have been the form mentioned above, signed by the dealer at the time of delivery and countersigned by a notary public), and for copies of the receipts showing use.
All of the above normally applies to people who live in California and ultimately bring their RV back to California, and who normally register their RV here. For clarification, there is no requirement to form an LLC or use it to purchase an RV in order to be able to take advantage of the California 'out of state delivery' provision.
Your situation is quite different in that you don't live in California and at most might be travellng through the state en route to somewhere else. Given that, I fail to see why you would need or want to pay high California registration fees. It would seem "logical" to re-register the RV in Montana, which would mean that the "pink slip" (proof of title/ownership) would be changed to Montana, and then you'd pay the annual fees to Montana. Many LLC owners use their LLC lawyer to handle the title and pay the registration fees, and to obtain the tags (equivalent of the UK tax disk). However, you might want to check out the costs of re-registering, annual fees, etc and compare them to continuing to pay annual fees to California; You might decide it's not worth changing anything.
Where folks seem to get in trouble is when they legally reside in one state and register their RV in another state (such as Montana). Their 'home state' can (and some do) claim that the LLC was formed specifically for the purpose of avoiding the annual fees. Since you have no legal residence in the USA, I don't see how any state could have that recourse in your situation.
Be advised that the above is merely an opinion and that neither I nor anyone here can provide legal advice.