If you'll re-read my post, you'll note that I stated that marines served aboard flagships *AND* capital ships. In fact, this was part of the rules and conduct of the C.S. Navy and the C.S. Marines (as well as their northern counterparts). Capital ships are major naval vessels, which included some ironclads. This is not to deny that the exigencies of war often necessitated the deployment of marines in other facilities, in the same way that C.S. Army troops were often detailed to perform marine duties aboard some ships.

Your "floating barracks" are known as "Receiving Ships" in naval parlance. Although it was common practice to house transient sailors in receiving ships, I am unaware of any naval station that utilized a receiving ship as a permanent marine barracks. The term "marine barracks" was not used to simply refer to a dormitory; it was a term applied to the facilities of the marine detachment which was organic to a naval facility, and included offices, armory, etc., in addition to a traditional "barracks".

And before we leave the subject of receiving ships, it might be of general interest to note that the quasi-permanent home of the C.S. Naval Academy was on board the C.S.S. Patrick Henry.