Look to people who live in a camper year-round for ways to accomplish this. Just an example:
https://www.followyourdetour.com/changing-your-domicile-to-texas/
If these people get audited by CO, it's a slam dunk that they're still CO tax residents, subject to CO income tax. They even (stupidly) say so on their website: "...our home state of Colorado, which will always be our home base for travel."
Each state has its own factors that they'll look at, but near the top of the list is usually where you have a home (apt, room, etc.) and where you spend most of your time.
You need to establish domicile in a no tax state by living there. If you don't, the state you're attempting to separate from will likely still be your tax home.
I think the fact that people get away with faking a change of domicile with these waste-of-time tricks leads to this misconception that you can officially change your tax residency by filling out some paperwork and getting a mailing address.
Just because the Texas DMV will accept two pieces of paper for a drivers license doesn't mean that the CO DOR will use the same standard. It won't.
I'm not saying don't do that, but don't think it will be defensible in the slim chance you get audited.
If you don't want to take the risk, look up the factors that your state considers to determine domicile/tax residency and make sure to address all of them that you reasonably can. It's honestly not that hard and not that expensive.
It is way, way easier to have a legal permanent residence, even if you're barely there. I would have something, whether it's a small studio apt, your dad's basement, or whatever.
I think you only need that for a period of time to demonstrate that you've established bona fide domicile in a new state. Once you've done that, I've found it's not necessary.