Length contraction, time dilation, and Lorentz velocity transforms; why don't any of these effects show up when I drive down the highway at 70mph?
They do show up. The fact that the speed is such a small fraction of the speed of light means the effects are far, far too small for us to notice.
These effects only work in space. The effects will show up on spaceships, but not on Earth.
These effects caused problems in the early days of police trying to regulate traffic. In 1953, a device that offset these effects was required in all new cars made worldwide. It is possible to see these effects in cars from before this time, but is illegal to drive them on the road without these devices.
These effects are valid for atomic size objects only. Anything large enough to be seen without a microscope does not experience these effects.