Avoid area distortion when moving features

Posting my own solution in case it helps anyone else. I needed these inset states in the shapefile for my own use, so the comments weren't too helpful. I found that the distortion arises when the global map coordinate reference system is different from the one for the layer. To fix this, I first changed the projection used by the layer to get it to how I wanted it to look and then reprojected it to the global CRS.