When I first read your question it seemed like it would be an easy one to answer. However as I started working on it I've changed my mind.
It appears when you add the MOVE argument to the COPY command it overrides other arguments such as UPDATEEXISTING. In other words adding the move argument means it will move all selected source files to the destination whether they are of different sizes or not (which is just what the help manual says). However I would think if the MOVE argument followed the UPDATEEXISTING argument then it should move any files which are qualified by the UPDATEEXISTING argument. But that's not what happens.
So the closest I can come to what you want to do is this:
Copy UPDATEEXISTING=size WHENEXISTS=rename
Which will rename the new qualifying source files (files of different size) when they are copied to the destination. It doesn't move them however.
I could write a batch file script that would take the files currently selected in the Opus source and do it that way, but that seems to be an overkill solution right now.
Of course there's a good chance I'm overlooking something obvious here so perhaps someone else might come up with an answer.
But if no one else does come up with a solution I believe this would be an excellent candidate as a feature request.