"does this mean that the ISS doesnt orbit the earth but rather the earth is spinning beneath it?" - R
No, the ISS has to orbit the Earth to counteract the Earth's gravity.
"sounds fair but the iss is supposed to be moving much faster than earth. or does it move just about 700mph in opposition to the earths rotation, causing a relative speed of about 1700 mph?" - R
Gravity is trying to pull the ISS to the surface of Earth. To counteract that effect without the need for continuously firing rocket engines the ISS has to travel perpendicular to the surface of Earth fast enough to maintain its height. So for every 1 metre that the ISS falls to ground it needs to have moved along far enough so that it is still the same height above the ground (the Earth's surface will fall away as the Earth is a globe).
"in that case, i would think the hypothetical gyro-box would wind up stuck to the walls and move around a bit as it resists the change in inertia/direction." - R
If you held that same gyro box on Earth about head height and then dropped it, what would happen? It would remain orientated in the same direction but it would drop to the ground, because of gravity. It would remain orientated all the way to the ground whereupon a collision would occur and those forces would overcome the power of the gyroscopes and it's orientation would alter.
In space, in the ISS, the box would fall like it does down here but there would never be a collision with the ground because of the lateral movement of the ISS (and the box inside, along with the gyroscopes). It just keeps on falling...
