Go to the Celebrity website and go into "quick reserve". Pretend you are booking a room. In the room category put "no preference" and it will list every room available. That is how I upgraded myself from a 1B to a Category 3 for a July Infinity sailing.You just have to pay the difference in price. I think the only time you can get free upgrades is when you board, but I'm not sure. I'm sure it helps to have a list of the rooms available before you board when looking for an upgrade.
The ships all sail full, they will grossly discount to travel industry employees to fill the ships. This occurs 30-60 days before sailing. Alaska has been in a big oversupply the last few years. Some excellent deals to be had!!!!