I’m sketching a big band arrangement starting on a grand staff. How might I label notes in a chord as (for example) Tenor sax1?
I one had an old conductors condensed score - you might see these labels
see example
You can create a paragraph style for this. Then use Engrave mode to fine tune the placement. Nothing automatic nor really easy here 
Make sure you save that paragraph style as default. Then you will be able to give it a keyboard shortcut, which streamlines the process a lot.