If you're on the outside, there is very little curve/spin. Make it big enough and it will almost seem like you're walking forward in a straight line. The closer you get to the center, the more you have to compensate for the spin.

What? I think you're confusing curve and spin which are very different things. You're sort of right that at the edge of the circle you have to compensate for the curve less, but the spin (defined here as the degrees of rotation per period of time) is exactly the same, and the tangential velocity is going to be much greater.

Every point on a solid circle is going to be turning at the same speed, that is a point near the center covers 90 degrees of rotation in the same period of time as a point on the very edge.

The farther you are from the center of a circle, the larger the distance is for each degree of rotation.

So say you have a circle that's large enough that one degree of rotation on the very edge covers a distance of a mile. Now let's say it rotates once per minute. If you're near the center of the circle where one degree covers a few inches, you barely have to move to keep up with the spinning of the circle. If you're on the very edge of the circle you'd have to run at 360 miles per minute to keep up with it. It would feel like you were running in a straight line, yeah, but you're not about to keep up.