Not being able to move the labels is most likely related to the position where they are at and JMP isn't able to pick them correctly (a bug). Axis settings also seem to be quite buggy with Ternary Plot. You cannot for example right click them to access axis settings. For example in Graph Builder you have access to more options like Edit > Copy/Paste Axis Settings.

For labels you might have to workaround the issue using hover labels and pinning them

You can try to clean them up with Hover Label editor

You can also tinker around in right-click customization menu and first Force labels Label to Values then move them and then change them back to Label by Row.


-Jarmo