@robert.down's approach works if style_light did not use elements basic to bootstrap. But it does and that clobbers bootstrap badly. So we start with existing stylesheet, let bootstrap override what it needs and then apply our lipstick on resulting pig.
Our objective was get away with standard stylesheet coming from globals/user preference. For standard codebase, it may be worth replacing
<link rel="stylesheet" href="<?php echo $css_header; ?>" type="text/css">
by a php include that provides a standardized way to manage css. That will give more flexibility to act on user preferences as well as vendor package changes etc.
On selfish note, it will give us a central place to add extra code to every script if needed.
In any case, for a casual developer css should be a single line somewhere before start of body tag.