For example, what I believe I'm seeing is that the stroke-width in a style attribute is being multiplied by the scale in a transform attribute. If true, then is there a function (similar to apply_transform for paths) that I can use to "un-transform" the style?

If you have applied the transform, then I think it should no longer multiply the stroke however I have not checked that inkex does not do that. 

SVG itself has vector effects which can exclude any scaling of strokes.

https://developer.mozilla.org/en-US/docs/Web/SVG/Attribute/vector-effect

I raised this question because I did an apply_transform() on the PathElement and it modified the d attribute as expected, but not the style. I looked through the source code and didn't see any evidence of apply_transform() operating on anything but the path.