In how many dimensions is the full-twisted "Mobius" band isotopic to the cylinder?

I think they are isotopic in $\mathbb R^4$. Consider a circle embedded smoothly in $\mathbb R^4$. It has a normal bundle with fiber $D^3$ and boundary $S^2\times S^1$. Given a band, such as the twisted or untwisted ones in the question, you can think of one boundary component of the band as an embedded circle in $\mathbb R^4$, while the other boundary component lies in the boundary of the normal bundle. This gives a loop in $\pi_1(S^2)$. Such a loop can be homotoped to a point, since $S^2$ is simply connected, and this homotopy will give a fiber-preserving isotopy untwisting any band.