It took me twenty years to understand the problem of time dilation, and a simple idea to see what's wrong with it. But the simple idea didn't come easily, it came after twenty years of struggle. So I can't expect a lot of people to understand what I'm saying. I'll reply to your post because you seem to have both a genuine intereste as well as the knowledge to either understand the problem or show me where I'm wrong.
The essence of the problem is, how do you measure the speed of light from a single frame of reference? Unless you could travel faster than light, obviously you can't. So to measure the speed of light from a frame A you need a frame B that is not moving regarding A.
So far so good. But Einstein said there was a problem if you introduced a third frame of reference (C) which is moving in relation to A and B. According to Einstein, C would not agree on the speed of light measured by A, but C must be wrong because we know that the speed of light is the same for all inertial reference frames. Therefore you have time dilation and the rest or SR and GR.
Now, wait a minute. Isn't there something wrong in all that? First, Einstein talks about the speed of light as measured between A and B and seen by C without taking into account that A and B are moving at different speeds in relation to C. Maybe there's something I'm overlooking but I couldn't come up with a single geometrical setup that would satisfy the criteria that A and B move at the same speed compared to C and do not move compared to each other. You can try that yourself, I'm quite convinced it isn't possible.
What I found about Relativity is that it basically says that if you measure things the wrong way, you get wrong results. The theory is right, the only thing that is wrong is that people think it's a theory about the universe when it's just a theory about measurements.