I need Customizer to write to a css file.

So here's my situation. I want to make a theme that is completely customizable through wp customizer. That includes everything from background colors and images, padding and margins, borders and radius, fonts and font sizes, opacities, etc... ect... I have managed to build the theme, but the one big snag I'm running into is the only way I know to output the generated css is by using wp_head action. That would be okay for a few lines of styling, but what I'm doing could easily generate a few hundred lines. What I really, really need is a way to write the generated css to a file upon saving the customizer settings.

As best I can tell there is no way to do it, as there is no action associated with saving customizer settings, to hook into. But I'm not one to give up so easily, especially when I have the wpmudev team on my side and I know you guys are pretty darn smart.

I'm open to any and all suggestions.