In reply to moving the floater. As a rule with my floater. He goes to what we call "The Borg" (So called as the managers spend half their lives looking at it, possibly for inspiration!) Or as others may know it as The Available Duties Board, and picks a duty that he fancies doing rather than the guy who wishes to come in on overtime. If he doesn't fancy any, he informs the guy he does not wish to move, and the guy who wishes to come in either takes his day-off or covers as reserve picking one of the available duties. In our office on a dailly basis, that normally goes into double figures.
In my case, the floater pleads with me to come in nearly every week as he detests my duty!