The command structure of Coastal Forces is a topic which to the best of my knowledge has never really been covered adequately to date, since as you rightly point the emphasis has tended to be one the boats and individual operations of flotillas. Indeed the command structure of Coastal Forces, is Coastal Forces, and is the body bearing the title, and which essentially underpinned all the personnel, all the boats and all the patrols made by those boats and their crews. Coastal Forces for example was responsible for all of the selection and training of its crews, as well as overseeing the construction of its boats, and their operational running once commissioned. This is why there is no such thing as 'German Coastal Forces' or 'Italian Coastal Forces', because it's not about the type of weaponry or technology used, nor the kind of warfare engaged in, it's about a specific organisation, or branch of the Royal Navy bearing the title as the first and only one ever to do so, and initially placed under the command of its own Rear-Admiral, Piers Kekewich, in 1940.
There is some very good stuff on the organisational structure of Nore Command in The Battle of the East Coast by J P Foynes which I will endeavour to scan and send you. Foynes states Watchful was originally the home of an Naval Officer in Charge (NOIC) and minesweepers subject to the First Officer in Charge (FOIC) Harwich, but that in July 1940 it was upgraded to a FOIC's base with Admiral Fullereton in command. Now as to the nature of his command within the port, I couldn't really say, but imagine the day-to-day operations of Coastal Forces and Minesweeping would have been handled by their respective Senior Officers or base commanders, with any overarching concerns of Nore coming through the FOIC, who would naturally have outranked the various base commanders.
Hornet was the first Coastal Forces base to be set up, if you discount the earlier use of Vernon, and definitely was an operational base. I think, and again I'm by no means certain, that it's 'headquarters' status possibly derived from the fact that Hornet was considered the principal Coastal Forces base, where unassigned personnel were sent for the purpose of administration. For example CF personnel returning from operational areas abroad would be posted there, and function as spare crew and the like before being moved on elsewhere.
An interesting subject!