Since I try to cruise about 3 times a year, I will chime in with my two cents.

If you are looking for a bargain cruise, forget NYC. Most of those cruises are sold well in advance and for close to full price. Galveston has had some great bargains and the air cost should be about the same as to Florida.

The "largest" cruise ship you heard about was the Queen Mary II. No real bargains there (and certainly not much for kids) unless you book one of the transatlantics. That entails one way air to or from the UK.

Try Vacationstogo.com. They have some heavily discounted cruises 90 days before cruising.

With kids, Royal Caribbean probably has the most activities-rock wall, ice skating rinks, etc. BUT Royal Caribbean and Celebrity are no longer offering much in the way of discounts through TA's. I have heard great things about Disney's kids program, but you are correct, they do not discount much, as they are sold out.

Look into NCL. Freestyle (meaning no formal and no fixed dining). And they are supposed to have a decent kids program. Carnival may be tooooo much of a "party hardy" atmosphere, unless you cruise during the summer. Don't need to expose the kids to a drunken party. My one and only Carnival cruise looked like an overgrown frat party. People were actually pouring beer from a funnel off someone's balcony to their friends on the deck below. And the "hairy chest" and "belly flop" contests were disgusting. Could be my age (55), but I was truly appalled. It would have been a hoot at 25, but NOT for families or us ADULTS.