So, just thinking out loud about this a little more,

If much of the issues arise from the angle between the camera and the surface,
I'm wondering what sort of improvement there would be if the scene were done
with an orthographic camera, but set off to the side by some angle.

Then you'd get an oblique view of the slice, and the ray-object intersection
that the solver would have to deal with wouldn't hit the same issues.

Then you take that render and scale it to stretch it back out and faux-undo the
angled view.  Perhaps if it only required a few degrees offset, it might not
introduce significant distortion.

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