Incredibly creative idea, I really enjoyed reading the question alone so I do hope you'll mature this into actual narrative work sometime (keep me updated if you do !).
With that being said, here are my suggestions, focused on travel first and navigation second :
1. Travel
Given your premise allows for its inhabitants cognition to alter the (pseudo ?-)physical shape of their universe, one very simplistic and instinctive means of travel I could think of is this :
If you know what the location you are trying to reach looks like and how far away it is, you could just meditate hard enough until it either forms in front of you or the physical space between the two locations is reduced.
This brings immediate advantages to mind, like the fact that travelling would be pretty fast and easy this way, with minimal risk from the everchanging surroundings. Just summon your destination intensely enough, and it's there.
As far as how to do that goes, you could gather a sufficient amount of people to collectively summon the destination (maybe as a civic duty ?). Or it could be an ad hoc summon, for example once the King has gathered an army he wants to send off somewhere, that army medidates collectively to reach its target. Alternatively, you could also have an order (of clerics maybe ?) dedicated to meta-meditation, who train during their entire lifetime to be able to summon geographical locations or "erase" massive swaths of land.
2. Navigation
The matter of navigation is a bit more tricky, because all forms of navigation (except the sense of orientation maybe) relies on physical phenomenoms used as comparative landmarks (the position of the stars, magnetic waves, GPS location, radiolocation, etc).
However, in this universe there could be a total absence of physical, permanent elements to base your landmarks on.
Maybe instead of physical rules navigation could then function using logic or instinct. 140
For example, maybe someone eventually discovers that your universe's constant evolution is in fact cyclical, and that certain locations are reported to regularly find themselves in one specific place. Given that, you could simply keep the directions these locations are in inscribed in an almanach, giving you the location's position depending on the time of year.
Or maybe some people are born with an innate sense of orientation, that allows them to guess the destination and then point the travellers into the specific direction. We could elaborate on that, and imagine a "profession" of sorts in which people from a given country/province have a constant instinct of where their home province is whenever they're abroad. These 'compasses' could serve the King as directional advisors, pointing him towards where they feel their homeland currently is. They could be foreign ambassadors, or maybe slaves captured for the purpose of orientation.
Otherwise, your ideas with the stars or the magnetic pole aren't bad at all, but the problem I have with them is that they are physical markers but somehow uninfluenced by your universe's constant fluidity unlike all other physical things, which means you are bending your own rules a little. That's completely fine, but I thought I would try to think of alternative ways to solve this problem.
Really looking forward to wherever you go with this ! 140