Is there a way to automatically refile highlighted text under an
org-heading? i.e. to cut the highlighted text and automatically paste it
under the heading of my choice?

You could call it org-refile-region. Similar to org-refile, but to refile
not the entire subtree, but only the highlighted region under any heading
in the current document. Ideally this would offer me only headings in the
current document.

Here's a start:

http://stackoverflow.com/questions/25256304/in-emacs-org-mode-how-to-refile-highlighted-text-under-an-org-heading

Thanks!