Good point.
The split is performed by the splittag.plugin.js put together by @Spuds.
Adding a button requires some moving around of stuff, but it's not too difficult.
If you want to give it a try, replace the splittag.plugin.js file with the attached.
Then, in jquery.sceditor.css (or even in custom.css) you add something like this:
.sceditor-button-splittag div {
background: url('../images/bbc/splittag.png');
}
pointing to the image you want to use (or using the base64 encoded image as background).
And finally, in Editor.subs.php, you can add the button, for example replacing:
array('spoiler', 'footnote'),
with:
array('spoiler', 'footnote', 'splittag'),