It would be helpful if you let us know the heat exchanger TEMA type. There are many varieties of floating heads. A couple of types which may fit your description are pictured below. In each of these types, there is an inner head and outer head whereby the tube fluid is contained in the inner head and the shell fluid is contained by the outer head. The outer head is what I think you are calling the floating chamber. These types do not seem to rely upon the tubesheet sliding on a gasket and maintaining a seal, nor do they use packing to prevent leaks to atmosphere. I'm not a heat exchanger guy, so maybe someone can enlighten me as to the correct terminology.
Are either of these similar to your heat exchanger?