It now looks like this:
As you can see, there are some issues with scrollbars and I still need to do things like turn on line numbers and what not. Code folding and syntax highlighting goodness are all there now though.
If anyone would like to do up a Kate syntax highlighter file for the plasma-desktop scripting, that would be truly awesome. The syntax description XML dialect is described here and the plasma-desktop additions to the standard ECMA script runtime are here.