Claudius suddenly gets real clear and direct once he starts planning. He’s all double talk and long clauses in longer sentences until a plan kicks in and then SPLAT. This is it. Crystal clear. As if he had it ready. But he can’t have had this plan ready, can he? He didn’t seem to know about Laertes’ return. Or Hamlet’s. He thought this was all over. And then Laertes turns up, ready to claim the throne and while Claudius is putting out THAT fire, Hamlet sends a letter that he’s back and ready for a reckoning.
All these years, I’ve thought of this as just a plan to get rid of Hamlet but it occurs to me now that this plan is ALSO a clever way to get rid of Laertes, who is also a threat. He can either get rid of Laertes by accusing him of murdering his nephew once the deed is done – or by getting him killed with an unbated sword in the duel. Maybe even slip Laertes the poisoned drink when he’s not paying attention.