Welcome, Darkwing! Hopefully, Saint Canard can be spared the worst of the Apocalypse.
We don't often see newbies to the game, so perhaps you'll let me sketch over some of the things that come up again, and again?
Bruce as time-traveller has been argued over for, well, decades. Is he visiting the future? An alternate Universe? A possible future? Does that future change every time he "returns"? It gets messy.
Then you have the "Is Bruce Good or Evil?" discussion. Which gets even worse
And when you refer to "shelters", do you mean bases? Or the places where a team's cryotubes are hidden (usually called boltholes). Again, the exact structure of the Morrow Project has ben argued over. It's usually best to go with whatever works for you and the players
Having said that, an active chain of command is something that a number of Project Directors have experimented with. It's sometimes referred to as an "awake" or "semi-awake" Project. It has advantages and disadvantages.
Personally, I like the idea of a "semi-awake" Morrow Project consisting of something like a specialist Task Force (probably with about 200 to 300 people)
And - if you want an example - Recon CA-4 is an ongoing example of this sort of thing
http://henrick.com/ca4/ I recommend it.
Matt W