Except, you know, that the rule section you quoted yourself states that Battery armament is only used when firing on ships.That is incorrect. The Attack Pool is constant. Battery is divided between your Ship and Squadron Batteries.The meaningful difference, I believe, is not in the words add and increase, but rather battery value vs attack pool.I can see that.
If we have Add not mean the same thing at all times then what about While, When, Before, After, etc?
Sure Add could mean a common definition but that is why I believe they use Increase. That way there is no confusion.
From Page 1 of the Rules Reference Guide.
Armament
The attacker’s armament indicates the color and number of dice that can be used during an attack. Anti-squadron armament is used when attacking a squadron. Battery armament is used when attacking a ship.
• Each hull zone of a ship has its own battery armament that it uses when the ship attacks from that hull zone.
• Each squadron has a single battery armament
• A ship has one anti-squadron armament that is used regardless of which hull zone is attacking
It still needs the word increase for you to have a proper sentence.
My concept is just a simple rule of thumb not something changing the rules