No, the problem is probably that, as you custom input is inline, it takes precedence, but when aggregating it, that higher weight gets lost. What I would try to do is add an "!important" indicator to the custom CSS.
Regarding JS optimization (which is the combination of aggregation and minifying); you'll have to be a bit more specific I'm afraid. What doesn't work? Any plugins you're using which are broken when JS optimization is on? Did you try with "force in head" and/or "look only in head"?
frank