After creating/saving an activity, re-opening it to edit won't allow links and drop-downs to be changed
I'm happy to report that the original issue was resolved with an update to 5.5.1. With this update made, the errors illustrated in my original post are no longer occurring.

Because we've long used CiviCRM without this error and first noticed it with 4.7.31 (and consistently with subsequent upgrades), we believe that this new upgrade has returned the functionality enabling us to again edit activities from a popup window opened from search results.

@RayWright, thank you for suggesting the java review and screenshots which helped us see that the issue was limited to "pop up" edit windows (i.e., activities opened from searches) rather than full-screen edits (i.e.,activities opened from reports). The latter may especially be helpful as a workaround if future users see this issue.