Swaying keel? Are you serious?
I hope you didn't buy a used lemon. I have a '78 C27 and have never heard of a swaying keel. This sounds like you may have a serious structural problem. I recommend calling Catalina Yachts tech. department (Phone 818 884-7700). I would sand/grind away the paint and any fiberglass around the keel/hull joint to make sure that paint and fiberglass is not all that's supporting your keel.