How to make a connector's label orientation persist when the connector moves?

[Orthoducks]

I am creating component diagrams which contain many diagonal connectors with labels. The labels need to be oriented horizontally. I know how to rotate them, but when I move a shape attached to a connector the connector moves, its slope changes, and its label's orientation changes with the slope.



How can I make the labels stay horizontal, once I've made them so? It seems to me that I'm looking for a way to tell Visio, "This connector's label is oriented relative to the page, not the connector," but I'm open to any solution that works.