Is it possible to label (or otherwise mark) a spot on a TRACK, rather than on the timeline - so that when the track gets moved or edited, the label or marker stays in its relative position on the track?
Once you have your label track below the audio track, click the Sync-Lock Tracks buttons. Now, when you move the audio the labels will move with it.
A trick I use is to make a Split at the point I want to mark. This creates two clips so you have to be careful when moving the audio (to make sure you move both clips). This has the advantage of not needing a label track and remembering to enable Sync-Lock. It has the disadvantage that the splits can’t be named/labelled.
Yet another method if you don’t want to remember to enable Sync-Lock is to include the label track in the selection (hold SHIFT then press DOWN arrow). This works except for inserting or generating audio.
Thanks to both of you for your help!
Follow up question: If I have two (or more) stereo tracks, each with their own corresponding label track, can I sync-lock the pairs without sync-locking ALL of the tracks together?
Each label track defines a sync-locked track group. So the answer to your question is “yes”.
See: Audacity Manual