Is there any keywords for asset listing that allow the user on the frontend to be able to change what the list is sorted by ?
You've got the code… read it. <grin>
But the short answer is no.
Yeah, yeah, so I am lazy 
Is there any way through the query string you know about ?
You cant sort asset listing using a form var submitted on the frontend.
BUT
It seems like the kind of thing asset listing should allow the user to do, and would have to be put in anyway once the search_page starts inheriting from it.