As Still said, it's probably slopping side to side and will need new bushings next time you haul out. It's not a huge job.
If you can get access to the top of the case with the board down, you could push a wedge (cheap rubber door-stops are ideal) either side of the plate as a temporary measure whilst sailing and sleeping - but don't forget to pull them out before trying to raise it again.
Bear in mind that a banging keel it's not only noisy but slow (you won't be winning any races with the board flopping around).
From RFC 1925: "(3) With sufficient thrust, pigs fly just fine. However, this is not necessarily a good idea. It is hard to be sure where they are going to land, and it could be dangerous sitting under them as they fly overhead."