I like the idea of tactical superiority quite a lot. If we then had black ops and secret service, it would make sense that those could even take out the tactical superiority group since tactical superiority is otherwise the battlefield ruler, basically. The anti-lots-of-ships role, anyway. It would kind of make me not want the cruisers/whatever to get the tactical superiority folks, though, because then there's too much getting them. I'm not sure what that would do to their role.
In terms of the ship roles having too many things, I agree that 5 is too many if all roles are effective against all roles. Aka, 3 relationships from each is too many. But if there's a "core three" and then an "extended two," that might work. The core 3 could be the main "battlefield units," whereas the other stuff is for other purposes that is somewhat tangential (off-battlefield duties).
One version of this:
Core trio for battlefield use:Tactical superiority
Cruiser (definitely a rename, and likely won't get the "big scary" stuff anymore)
Black ops (now probably needs a renamed)
Specialty two:Demolition - anti-building, but not going to win against anything in the core trio on its own. Can certainly HELP, but it's not going to do it on its own.
Giant killer - goes for the "big scary" stuff, instead of cruisers being able to do that. Functions like the bomber in that it can help in main battles, but it's not a core battlefield winner.
Other two same as original quadrangle:
Structures: is actually a ship class, and it's what demolition stuff kills.
Big Scary: is also actually a ship class (maybe called Leviathan?), and it's what giant killers are best at dealing with even though these things wreck everything in terms of metal for metal.
This way the quadrangle is simplified in some ways, despite being split into more parts.