Okay, so I am sure there are a million better ways to do this, but this is what I have done and it seems to work for now. Since "sortable" doesn't update the indexes that tabs uses for deleting and such, I am storing the index that the plugin is expecting when I create the tabs (the index "tabs" originally gave each tab). When you remove or add a tab, the indexes are again updated, so when you do this, you need to also refresh the indexes you stored. Here is how I am doing it:
var i = 0;
$('#tabs').find('li').each(function(){
$(this).data('tabIndex', i);
i++;
});
As you can see, I am just indexing the same way that "tabs" does when the tabs are created, so that I have the same indexes it does. When you do this, you can just get the id of the tab you want to delete and call $('#tabId').data('tabIndex') to get its original index.
I hope this is helpful. I tried to find a better way to accomplish this, so if someone else with more experience can figure something out, please let me know.