This adds an option to make the 3D viewport track to the Z axis of the 3D cursor when Lock to Cursor is enabled. It's a work-in-progress, as I need to iron out some wrinkles with quad-view and what angle the viewport is restored to when the option is disabled, but it's functional enough to show off. Here's a quick video:
And an update clip:
When this option is enabled, users can take advantage of transform orientations, axis constraints, numeric input, and incremental snapping when they rotate the viewport. While I used a keyboard shortcut in the video, I see this working fairly well with a 3D cursor gizmo as the primary point of interaction.