The biggest improvement is that we'll now insert each parsed JSX script
back into a `<script>` tag with the body set. This allows the browser to
execute these scripts normally. Using `Function(functionBody)` or
`eval(functionBody)` both execute in window scope, but `var` assignments
don't actually get set on window (unlike everywhere else).
I also did some cleanup to make the code a little bit more readable.
In my minimal test cases this didn't break anything (scripts loaded in
the right order).