I don't think you have to wait 18 months with the HH cards. I've read reports of people getting them again after 65 days.
It's not necessary to close the HH cards to get the AA cards. The only reason would be if you think Citi wouldn't want to extend more credit to you. Your plan of swapping out cards every 2 years sounds pretty good, but you may want to keep one card just so you can establish a long term, on going relationship with Citi.