It seems like, when moving tokens in Mipui that I need to manually cut and paste the contents of cells. Is this accurate? Is there a simpler/faster way to move tokens?
Use the token mode
When using the Token mode instead of Select it's possible to mouse over the existing token. In the top-left corner of the token there is a small white square. Move the mouse around until it turns into a white four-directional arrow. That is how you can drag the token around instead of cutting and pasting.