We are also a family of 6 and our best option was two connecting Category 10's. The only rooms accommodating a family of 6 are categories 1 and 2. These book up far in advance and are also very expensive.
We are a family of 5 (one being an infant) so we decided to bring our live in babysitter (making us 6) and get 2 connecting Cat 9 rooms. It's costing us about $4500 (including transfers but without air) for both rooms for the 7 night cruise on 4/27.
A suggestion is looking into getting 2 "secret porthole" rooms that connect. That'll will save you a little money and you'll still have a window. Thank Barbara (platinum castaway club) for telling everyone about those! Good luck!
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