I would like to model my scene with the perspective view showing a Solid shaded view, and the ortho views in wireframe. Pressing Z just toggles all my views; is it possible to make the viewport shading view-specific (I know I can create a new window and see a view in that, but I’d like different shading modes in the four quad views)?
Are you in quad view ? If so then that is just a single viewport split into 4 views. Any changes will affect all those views.
If you want to have different view settings then you need to split the viewport into separate viewports (Split a view by dragging the corner triangles or RMB on an edge to split the view)
You can have a rendered view in quad then use the Boundary render (ctrl B?) to limit the render in the other 3 views. I just make a tiny box in the corner of each. So I get wireframe in 3 views and render in cam view (or any portion of that I choose).