About time someone talked about blockade maneuvers. So this is what I have figured out not that I blockade all the time. Getting a maneuver gives a bonus score similar to clearing something in the puzzle.
First of all don't let blockade stuff get in the way of you playing well. If you can fit in one here and there and as you play more you will find you can fit in more and more. Better to get a good duty score and only a few maneuvers.
Bilge: So for bilge the blockade pieces do not have to be a part of a clear to be used. It is more about getting corresponding pieces onto the right level. But don't freak out just keep your eye on the blockade pieces as you puzzle and if you see them on the proper levels, then clear em. If you bilge well to begin with it will increase the number of blockade pieces floating in your bilge making it easier to find matches.
Carp: I have no FUCKING idea. Only if you get a blockade combo on top of a masterpiece that is like super awesome double score.
Sails: The trick for sails is to position the blockade pieces so that they can interact with pieces that haven't fallen yet. (If only I had a screencap) So say you are filling a bottom area point the blockade part UP so that it can hopefully come in contact with a piece that might match it. A large part of it is luck but you can increase your chances. Try not to hang blockade pieces where they can't come in contact with another blockade piece. In sails they have to be adjacent and part of the same clear to work, unlike bilge. If the blockade piece doesn't fit into your puzzle clear try hanging it off the edge and having a little combo underneath it. Again don't let yourself be so distracted that you can't play the puzzle well. Also it is ok to waste blockade pieces too, as long as you can get a few blockade clears in there basic good sailing will help you more.