Taming mouse-camera rotate behavior?

[micheus]

Starting from the end...

-- There seems no way to get certain views: For example, how do I position the scene so that the Y-axis appears horizontal on the screen, and the Z axis vertical? Is this actually impossible?

No. This is the way Wings3D used the axis.
During import and export you have option to switch them.

-- One mouse direction maps to a screen-relative motion, while the other maps to an model-relative motion -- rather disorienting.

I'm not sure. I would say that it's always screen-relative which we round around the centre of the screen (axis origin). Thinking in 2D screen, rotating around Y (left-right) and rotating around X (up-down).

Something handy would be to use View->Aim or View->Highlight Aim [A] to define a temporary centre for the camera actions (the Look At point). Just select an object element and hit "A" to centre that element on screen. Even if you pan the camera that will still be the centre for the camera actions.