I did it! I made tabs! Here's how I did it, using JQuery UI http://jqueryui.com/demos/tabs/.
In the main Ajax Search results tpl, I added:
$( "#tabs" ).tabs();
The div "tabs" surrounding the as.listGrpResults satisfied the requirements of a basic JQuery UI tabbed element. Then empty "tablist" ul gets populated dynamically from the groups themselves.
This is put in the beginning of the grpResult tpl:
var parent = document.getElementById('tablist');
var listItem = document.createElement('li');
var str = '[+as.grpResultId+]';
var title = str.substring(10);
listItem.innerHTML = '<a href="#[+as.grpResultId+]">'+title+'</a>';
The script creates and loads li elements for the tabs on-the-fly. The title is extracted from the as.grpResultId string by stripping the prefix that AjaxSearch adds to the value of the grouping TV. There should be some other way of getting the group title, but I couldn't find anything.
Anyway, aside from some basic styling, it makes working tabs of a grouped Ajaxified AjaxSearch, using JQuery.