I have to say, when I had it explained to me that everyone and everything was always moving at "c" and moving the vector more toward dimensions in space bled momentum from the momentum in time. It made a lot of things just make sense that previously did not.
Since you seem to know a bit about this, one thing always puzzled me. It would appear to me that there's not really an "at rest" state in terms of movement in space. We're on a planet orbiting a sun that orbits the central point of our galaxy, which in turn is also moving and perhaps orbiting something else even bigger. So, "at rest" is always subjective.
With that understanding, when we're not moving from our point of view, we're travelling through time at "c". But in reality, it's probably some lower value. Perhaps "0.8c" when viewed from the universe as a whole. But, that's fine because we're ALL moving at 0.8c through time, so who cares. But the twin paradox says if a twin travels away at a high speed then returns, they would have aged less. Bearing in mind all of the above, that makes sense, except for the general galactic movement.
Whatever is influencing us, there must be a 3d vector in space we, as a whole, are moving toward (probably constantly changing though). So, surely if you sent someone in the opposite of that vector, time for them would actually speed up rather than slow down. In fact, if you sent them exactly on that vector (and they followed any changes in 3d vector in real time) then returned. Would they not "catch up" and be on part overall with time passing?
Likewise, sending them on another vector would have the effect described by relativity, but there would be a skew from what is expected because the actual total vector would also be influenced by the speed we were already moving in another direction?
We wouldn't see this skew on satellites and the like because they're travelling with us on that vector but at a constant speed relative to us too. But sending away from us and back, we probably would. Or, am I again misunderstanding things on a fundamental level?
I waste too much time thinking about such weird things, I know.