Here's a quick and dirty way to html export (or any export) only the displayed levels of an outline.

1. Highlight the entire outline
2. In the console (F2) type tk_textCopy textcmd
3. Open a new outline
4. Paste either with Ctrl-v or Edit/Paste menu pick
5. The resulting outline should only contain the visible node from the first outline and can be exported to html or whatever.

This works by bypassing the special tkoutline copy to clipboard code and calls the standard text widget copy function. So only the text that is actually in the outline gets copied.