I would like to create a map in QGIS comparing the relative size and latitudes of Japan to the US. There are a few websites like mapfrappe which allow this using Google Maps, but I would like to be able to have more control over the map settings, projections etc. I like the idea of country comparisons, but I really don't like their execution. My goal is to give a frame of reference for possibly unfamiliar locations. If I discuss Hokkaido, it might be hard to visualize how far north it is, or how large it is. I could provide coordinates and area measurements, but if a large number of areas are discussed, people can start to drown in numbers, where a map or image can quickly provide easy to compare references.
I created an example using the Natural Earth coastline shapefile as a base and dragging the DIV GIS japan admin shapefile over to the east coast of the US (super crappy, but provides a quick visualization). I am not worried about area distortions because I don't want to change any latitude values, but I do want the latitude coordinates to be accurate.
What would be a better way to go about this in QGIS?