Bart B.,
Not that I am an expert on these matters, but I believe there is an error in your argument, but it is key to the discovery of relativity.
E = m c^2 implies time, because velocity is the derivative of distance with respect to time. And prior to relativity, save perhaps for Einstein's contemporary Lorentz, time passage was considered a constant and invariant with respect to space. Since the hypothesis to contrary has been applied, it has been proven repeatedly to be not so.
Once estimates of the speed of light were made by systems of instrument starting a couple of centuries ago, physicists were puzzled that the speed of light did not vary with respect to its arrival from moving sources of varying speeds (e.g., Michelson & Morley). Doppler effects were there for sure. Sources moving toward us caused shifts to blue and objects moving away shifted to red. But why did the "clock speed" c of light remain the same?
Further investigation revealed changes of spatial and "temporal" geometry. In effect, relative motion caused changes of clock speed.
The equations of special relativity were the ones that addressed some of the basic geometric relations, and ten years later Einstein came up with the General Relativity relations which are much more comprehensive.
For the moving body time t is distorted by the ratio of the relative speed to light velocity c in the following form. The
t' = t0 [1 - (v/c)^2)^0.5
Or the time in a moving body t' is reduced with respect to a body at rest t0 by a factor with the exponential terms.
Time is also distorted by the presence of mass and its gravitational distortion. And correspondingly, energy distributed over space will have the same effect as the mass.
For a photon, I guess you could say that time has stopped, since its relative velocity is c. But when you divide by zero, this poses problems. And in the case of a body like a black hole, a mass with no finite dimensions, but one where escape velocities can be defined in the spaces surrounding them at levels higher than c, then there is another instance of time stopping - and at lower radii from the center of this mass, doing something drastically different under the "event horizon".
If time can be dilated or stretched by spatial position to mass or energy or else by relative velocity, then I would argue that it exists. Its part of a cosmos for which there was an initial event or cause. It suggests, however, that the Creator resides outside of it - as much as in...
When it came to formulating all of this, Einstein managed to get a lot of mileage out of the notion of passengers in a railroad car or elevator who experience accelerations or force of gravity, but would not be able to distinguish between the tw, the so-called equivalence principle. We can use this as a segue to another idea - and that of the elevator being stuck. This introduces subjective time which seems to be in the background of this discussion: our own perception of time's passage whether exciting ( brief) or monotonous ( extended).
Ah, never mind
So having gone this far, we'll probably have to address free will, quantum mechanics and uncertainties another day...