Okay, if you want to call time "the continuation of existence", I guess you can.
This is experimentally falsified. Time does vary according to relative speed, acceleration, and gravity. The effects have been directly measured and the overall theory tested in multiple ways.
I can assure you that "the continuation of the universe' is not being measured with a clock directly, its output is independent of the "continuation of the universe". The effect of speed, acceleration, and gravity have an effect on that the clock and that associated with the speed, etc., but the universal now is still omnipresent.
It doesn't even have to involve forces, relative speed alone produces time dilation. A 'clock' can be any physical process that takes a known time, so, for example, it applies to the half-life of particles such as the fast moving muons created in the upper atmosphere, far more of which reach the surface than would be expected without them experiencing time dilation (see
here, and
here). The GPS system has to take account of relativistic effects on time due to both the relative motion between the satellites and earth, and the gravitational difference (see
here). The adjustments are precise and work exactly as the theory predicts.
Here is an example, a space ship with a clock launches from planet earth, goes immediately to C speed which is maintained in a circular orbit that gets it back to earth one year later and immediately lands. What does the clock on board the spaceship show when it lands, how many days elapsed? For a clock on earth, from the beginning to the end of the trip, how many days? .
Now if you say less than one day for the spaceship and 365 days for the clock on earth, that's correct, for the ship's clock has not been working for one year. At C speed, it is not like in the movies, everything at that C speed is pure energy, like light. The theory of a human not aging on such a journey is theoretically correct if all the atoms that constituted them came back together again as before, but good luck with that possibility...I don't think so..
Anyways, the point is that the clock can not count when it is reduced to energy and would show zero days. The ship experienced one light year, a light year is the same length as a earth year, the spaceship and observers both experienced one year of the universal continuation.
As I say, the 'universal now' is omnipresent, it is not a refutation of relativity as far as I'm concerned, but it would seem that way to those who interpret it the way you are, ie., the perfectly normally operating clock on board is measuring "universal continuation" directly
Why on earth would anybody do that? I don't mean to imply that you're not generally trustworthy, but this is a question of solid science and a theory that has been tested in many ways and is, in the GPS system, in everyday use. Why would anybody trust some random person on the internet above that?
Quite remarkable, then, that no matter what sort of 'clock' we use, they all behave exactly as if relativity is correct.
I am not discussing relativity, I am explaining that clocks do not measure the "continuation of the universe" directly, they do indirectly using a proxy human built instrument that counts pulses and outputs 'time' calibrated to agreed upon standards that correspond to finite periods of "the continuation of the universe".
It is not esoteric, it is simple and straight forward. So clocks measure "time" indirectly, the spaceship travel time is not affected by the output of a non working clock, or in the case of space travel at less than C, with so called 'time dilation', actual spaceship flight times will always coincide with that of base control, not that registered on a clock affected by the forces of velocity, gravity, etc..