While we can always find coordinates that make the metric Minkowski at a single point, it is not true that we can always find coordinates that make the metric Minkowski over a finite region, no matter how small.

Indeed; this is why the concept of an "inertial frame" does not exist in general relativity, except in the infinitesimal limit.

But as long as we're going to permit ourselves to speak about the motion of an entire rocket or person, rather than the motion of its parts (thus in effect modeling the object as a point-particle), we can equally well describe the same rocket or person as being at rest.