We hunt down cruises using vacationstogo.com website. They do most cruise lines and can sort by price/night/person. Sometimes we book through them as they are very good but sometimes take the info they gave and book direct.
Don’t dismiss Port Canaveral. It is not close #2 to Miami in departures and passengers and double Port Everglades.
Having your Klan arrive in Orlando, staying at airport hotel, and making 1 hour transfer to the port may very well be less stressful than Miami.