I think it'd be as unobtrusive as possible, visually speaking. After everything that's happened to the previous HQ buildings (bastards... ) I would think putting all the team's eggs in one basket with a big (even comparably big) monolithic building, even a well-defended one, would be a risky venture. The beauty of this idea is that you can still have great defensive systems, training facilities, and separate living space for everyone, and you can improve on the old HQ concepts by splitting everything up, spreading it out, and hiding crucial tactical and defensive assets whenever possible.
To the casual observer, the island should look like nothing more than a private island (political/economic loophole, btw!) with the typical accoutrements of a handful of wealthy individuals. Under the surface, you can arm 'em to the teeth, give 'em jumpin' party spots, do whatever you want. It'd be an interesting construction job - especially given the secrecy necessary - but when it's all done, this island could be made into a great big Wayne Manor for the whole team, so to speak. Given time and everyone's OK, I'd like to flesh the idea out a bit more in future posts in this issue (and maybe a few drawings and schematics eventually).
) I would think putting all the team's eggs in one basket with a big (even comparably big) monolithic building, even a well-defended one, would be a risky venture. The beauty of this idea is that you can still have great defensive systems, training facilities, and separate living space for everyone, and you can improve on the old HQ concepts by splitting everything up, spreading it out, and hiding crucial tactical and defensive assets whenever possible. 
