A variation on your idea is to have a server-side USER-AGENT detector
that will figure out what style sheet to attach to the page. This way you can have a firefox.css, ie.css, opera.css, etc
.
You can accomplish a similar thing in Javascript itself, although you may not regard it as clean.
I have done a similar thing by having a default.css
which includes all common styles and then specific style sheets
are added to override, or enhance the defaults.