“...the contraction effects are pretty negligible until you start getting to at least significant fractions of c...”
With natural means. But artificial means follow the logical path, that there is a speed limit, but no known limit to spatial or temporal contraction or expansion.
A thought problem for this is a time machine that can go either forwards or backwards in time, but can also either maintain its location relative to the movement of the rest of the universe (like a typical sci-fi time machine) or remain at its absolute location, as the universe moves around it, or moves its location relative to the rest of the universe.
So, for example, if it wanted to materialize in the same location as when it left, it would have to follow the very elaborate vectors of everything else.
But if say they wanted to go to the far side of the galaxy, as long as they maintain their absolute location, relative to the galaxy as a whole, they could go forwards or backwards in time, say 250 million years, yet end up on the far side. Then go in the other direction in time, but relative to the rotation of the galaxy, and still be on the far side, but in the current day.
Finally moving within the galaxy would involve calculating where your destination had been, or was going to be. So even if you are just going 1000 mph, eventually in time you will reach that point.
“But artificial means follow the logical path, that there is a speed limit, but no known limit to spatial or temporal contraction or expansion.”
But there is a known limit to spatial/temporal contraction, and it is inherently tied in with the speed limit itself. Photons are the perfect example of this. They travel at the speed of light in the forward direction, and thus the length contraction/time dilation (both the same thing really) reaches 100% for them in that direction. This reduces the dimension that they are traveling along to a single point.
So, if a photon had consciousness to perceive its surroundings, and started at the far edge of the universe, it would perceive a zero distance between its starting point and its destination on the other side of the universe, and it would perceive the travel to be occurring instantaneously, taking no time at all. You can’t contract length any more than that; there is no way to contract a spatial dimension beyond zero, because there is no such thing as negative space.
This is also the reason why your theoretical machine could never travel back in time through contraction, because time is, as you say, a spatial dimension, so there is no such thing as negative time. The best you can do is to freeze time for yourself while the universe around you spins on, but then you would have to travel at the speed of light, which you can’t do because you have mass.
Actually, let me amend that last part. I believe matter actually does travel very near to the speed of light, just in the temporal dimension, rather than the spatial ones. We’re the mirror image of the photon, because it is the temporal dimension which is, from our perspective, contracted to a single point. We can only perceive time as a single contracted point, while the photon can only perceive space as a single, contracted point, and I think it is for the same reasons, just different manifestations of the same phenomenon.