That is incorrect. They will not agree on the results of their measurement of elapsed time. If that disagreement is due solely to the effects of acceleration on the atoms of one of the clocks, then that is what is being measured, not time.
Not true, acceleration does not have to be present to measure these effects. In fact, acceleration adds additional time dilation effects (General relativity) that are seperate from and and addition to the special relativity effects. You can observe time dilation on clocks that are kept at a constant speed. And if you think phycisists can't take into account something as simple light travel time...you have very little faith in modern scientists.
Again with the observation of events, not the actuality of events. How a given observer observes an event has no bearing whatsoever on the actuality of the event itself.
Actually this has lots to do with the 'actuallity' of the event, as the observer is physically interacting with the system. If the light is a high energy bath of gamma rays, in one case he'll be fried by both at the same time. In another he'll be fried by one, THEN the other. The difference is a single intense blast, or a longer milder blast.... Observation IS 'actuality'. If we cannot trust what we cannot observe....then all of empirical science and experimentation don't hold up.
Currently, we have no idea of the nature of light
I beg to differ. While we do not understand it in it's entirety, it is actually one of the best characterized and understood phenomena in science today. And while we may have further breakthroughs in how light works in extreme circumstances, none of those results will completely invalidate the understanding we have today.
This feeds into my next point where you state:
In my opinion, the Speed of light = 1.802,265,898 MegaFurlongs / MicroFortnight relative to it’s starting point.
Okay, so now you're throwing out the constancy of the speed of light entirely? A basic observed fact since the 1900's (michelson-morley experiments), replicated in countless experiments with various designs, and the foundation of a lot of modern technology and put to use every day in things ranging from modern materials science (quantum physics uses this in understanding atomic structure and behavior), to computers and communications devices...
Okay MA, are you just pulling my leg?
As it is, if you refuse to accept this fact, the rest of this arguement is entirely pointless, as time dilation is predicated upon (and a consequence of) the speed of light being a universal constant completely independent of an observers motion and acceleration. I.e. if you cannot accept this, it's only logical that you don't accept time dilation, and I'm not going to argue the point further.
Also, I'm going to throw in another confirmation of time dilation for the curious (as I'm not going to argue the point with MA until we clear up the speed of light = constant issue): The lifespan of Muons created by high energy cosmic ray impacts in the upper atmosphere. These particles live a very, very short time. So short that in newtonian physics they do not live long enough to travel from the upper atmosphere where they are created, down to the ground observation stations at the speeds they are observed at. They should die before they arrive. However they DO arrive in very significant numbers, indicating that the half-life of the muons as we observe it is increased by the time dilation factor of their velocity. They still experience the short half-life, but since they move so rapidly compared to us they last longer, and are able to make the trip. Here is another concrete consequence of time dilation, that isn't just a reading on a clock.
And i'll anticipate a couple counter points: Yes, we do know they are formed in the upper atmosphere, not lower and Yes this is replicated in particle accelerators every time they do experiments in precisely monitored and controlled conditions...