Distance can absolutely be concrete. We can specify distance traveled by light in a vacuum, or, if you'd rather, a specified number of Planck units. Similarly, time can be defined by the number of wavelengths of a photon of a given energy level. Which is basically the definition of modern SI second and meter are derived. They're based on the speed of light.
In the end, all you're doing is finding different ways to dissect physical constants. But you're still using those constant. The constant itself doesn't change because the Earth revolves slower today than it did yesterday, yet the planet certainly does revolve the same distance about its axis in more time.
Which is why I say distance and time are not really variable or imprecise (better terms than abstract, which simply has to many nebulous meanings) until you start to introduce relativity.
In fact, time is a fundamental element of many physical constants. The Planck constant, the gravitational constant, and the speed of light are all fundamentally based on time and distance. And since the speed of light relates to mass and energy, whatever units you pick need to be consistent. If we say that 1 second is always 1/84,000th of a solar Earth day (instantaneously I suppose?) then you've immediately made 3 of the known physical constants depending on how quickly the Earth spins. And you could do that and recalculate all of physics every day if you wanted to. But it's kind of stupid. It would be like re-graduating a tape measure every day you build a house. In theory it's just fine. Practically it's really not.
