I suspect that if physics texts contained the amount of philosophical hand-wringing needed to satisfy you, they'd be twice as big and even harder to read. Similarly, one measures different spacetime coordinates for events in different relativistic reference frames, yet there are predictable relationships between the coordinates in different frames based on the relationships between the frames.
Theories survive because they appear to model the universe better than the known alternatives.
I like this better than Autodynamics. However, even he seems to admit that there's no experimental proof for his idea, and from what I can tell he isn't even making substantially different predictions than conventional theories, just trying to explain them in a different way. Two theories that make the same predictions in different ways aren't really different theories. However, scientists have tended to prefer the theory that uses the least extra stuff to explain what's going on. Misstating what Taylor and Wheeler say about spacetime interval isn't a criticism of the idea.