Hey badgerton,
I am afraid it is not possible using the Label tool. The labels are designed in a way that gives huge freedom and flexibility as to how someone prefers to use labels, but it is mainly focused on the workflow of having labels in a readable position.
However, if you are not afraid of some GDL coding, you can create your own label, that might be capable of just what you are looking for. If that's not your thing, there's an object called "Multileader Label 20". It is mainly for placing labels with multiple leaders, but you can of course use it with a single leader and rotate it in any direction. I have attached an example for you:
https://graphisoft.sharefile.com/d-sa96488901e840d78
Have fun!
Daniel Alexander Kovacs
Professional Services Consultant
GRAPHISOFT
For Troubleshooting and useful Tips & Tricks visit