I ended up making a couple of edits to quicktabs.js. At its most basic, in line 24 I changed 'click' to 'mouseenter' and changed the name of the quicktabsClick() function to quicktabsHover().

When the user clicked the link in the tab, though, the page refreshed; I added the following at line 25 (below the new call to quicktabsHover):

$(this).unbind('click').bind('click', quicktabsClick);

I also added a new function:

var quicktabsClick = function() {
    return false;
}