Basically I have a structure that used to work perfectly in 3.0.x and now it breaks with undefined variable errors.
There is a simple solution for the original topic. Your application and main css files should be scss files. That means you can use the known syntax:
/*
*= require_self
*= require main
*/
In main.scss you can import the partials like this:
@import 'partials/base'
@import 'partials/header'
These files are sass files and you can benefit from the greatness of SASS ;-)