If all you're trying to do is reassign this to an operator's worklist from a shared workbasket then Carissa's suggestion should work.
I'm just a little concerned about this requirement/implementation detail you mentioned. "How do we configure Pega so that if an Operator opens a case from the WorkBasket and saves, it is moved out of the WorkBasket and onto the Operator's WorkList?"
Theoretically, you could try to create/override your "Save" operation to do both at once, but I'm not sure you would want to actually do that. If you achieved this, then any operator (say, a manager) just trying to update a case and save changes would also inadvertently reassign the case to themselves. I'm not sure that's what you want.