I ran the Cordorian Navy for a good chunk of time, so I did want to put my personal experience regarding 'being inclusive' in the chatter here as an example of why I think the way I do about it.
Being inclusive doesn't always help. I would set up a table with a sign saying 'JOIN THE NAVY', I would post advertisements and updates on what the Navy was doing on the boards, I would take just about anyone and everyone who showed interest with the caveat they show up for a 'trial run' before they got their free sailing kit, the guard was always involved/invited, AND I would take the ship out every other day.
At times, this worked fine and the Navy really flourished. Other times however, we couldn't even scape together 5 people for the 6-requirement ship, with maybe only two of them having the actual skill investment.
The burn-out was absolutely intense. My character hired a couple others to also host sails in timezones I couldn't really swing myself and it rarely worked out for them or they moved on to something else for their own valid reasons.
I've seen this occur with two other Navies I was active in, the Andunorian Navy and the Merchant Navy. With both of them the Andunorian Admiral and Merchant Captain were incredibly inclusive but also had their rough stints where they could barely scrape a crew together for weeks at a time despite TONS of advertising and active recruitment efforts.
All of this is to give context to what I think the main 'issue' is. You can be inclusive, active, do everything 'right' and still have those patches of inactivity from the crew, because like everything else on Arelith (or really games as a whole), interest ebbs and flows. You see it all the time with races, trades and classes. There will be a BOOM of one specific thing that you just see everywhere for a while, then suddenly they're all gone. To either try something new, get involved in something different, variety is the spice of life. I'd go so far as to say it's unavoidable and everyone who runs a crew/owns a ship will face this problem at some point or another and it's not always a reflection on how inclusive you are or how compelling your story is. It's just a fact of life given we're all here playing a video game with options. We love options!
That said, having lower-requirement ships for lease within the same Navy Umbrella for Settlements would be a great way to weather these inactivity periods. Since in my opinion they WILL happen, this is a great option to keep those still interested going without stressing out whoever is running the Navy when it comes to numbers. I also really love the idea of a 'Crew House', perhaps putting the 'smaller' Navy ships there as temporary leases for whenever the crew wants to go out, Captain or not. I agree running it like a guard with a 'barracks' style situation where there's not as much emphasis on the time you HAVE to go out would be healthier for everybody, from those running the faction to those in the late-timezone play times who really wanna sail but struggle to get out on the water. Win-win-win across the board!