I know what you are trying to say.
It always existed, yet started moving, yet there is no start to the movement because it was always "starting". I know, I just pointed how this is a contradiction.
I think it's just going to repetitive if you keep just repeating your assertion to address the points to refutation of the assertion.
I know time only exists while it's changing. If it's always been changing, then there is the infinite chain and cause, if there is start point, it was not always changing, it was either still at one point then changed or it started (for example movement has a start). As for infinite change, it's show to be an effect. Every effect has a cause.
What is might be ever effect has a cause, is that state of the effect is not the cause, it has a previous state which makes the state.
Your trying to say movement doesn't haven't a cause, the effect it's cause, which goes against the principle. And you trying to say it is in time, but before that time didn't exist, and just make time appear with no cause, movement just appear, and not in need of a eternal uncaused cause.
I think it comes down to denying every effect has a cause, and your into semantics to escape that.
Anyways, the logic is valid:
Every effect has a cause.
Finite and infinite chains of effects, still makes the whole chain an effect.
The whole chain thus must have uncaused cause.
I think you have an issue with the first premise and saying some how it's not true, and I tried to show you the flaw in your reasoning.