Don't m.ove until queen is mated and laying otherwise you'll just be begging for disaster. You're right the timing is not good. Give it another week or two and check to see if you have a laying queen or not, if you do then move it. Sometimes they remove the remnants of a queen cell sometimes they don't for the most part they'll remove them. No point in requeening because they are taking care of that. If they don't succeed or the queen does not perform then you could requeen. If you take the inner cover off and let them sit for ten to fifteen minutes they should thickly cover the top of the hive but myself I would leave them alone. You don't want to disrupt the new queens orientation or mating flights! Others might do different but that's what I do.