I’ve looked into the Montana registration thing a couple of times, mostly out of curiosity. Yes, it can avoid sales tax, but it’s not as simple or risk-free as it sounds. If you don’t actually live or operate out of Montana, some states can come after you later for back taxes and penalties...
I've shipped a car across states before and I definitely get your concern about not having enough visibility. When I did it, I picked my own transport company instead of going through the dealer. Having direct contact made the process less stressful since I knew exactly who was moving my car...