Starships: Dreadnought Cruiser
. Heavy reconnaissance. Because of their power, the Invincibles could sweep away the screen of enemy cruisers to close with and observe an enemy battlefleet before using their superior speed to retire.
. Close support for the battle fleet. They could be stationed at the ends of the battle line to stop enemy cruisers harassing the battleships, and to harass the enemy's battleships if they were busy fighting battleships. Also, the Invincibles could operate as the fast wing of the battlefleet and try to outmanoeuvre the enemy.
. Pursuit. If an enemy fleet ran, then the Invincibles would use their speed to pursue, and their guns to damage or slow enemy ships.
. Commerce protection. The new ships would hunt down enemy cruisers and commerce raiders.
While in real life, battlecruisers were a dead end development evolved from the armoured cruiser, and eventually superseded by the fast battleship and it's roles theoretically usurped by the super cruiser, it occurred to me while chasing down every single capital in the early stages of the Great Patriotic War with a hunting pack of nine Admiral class, you know, a whole bunch of Hoods, that on paper, battlecruisers killed. Numbers helped.
Also noticed that the Italians and Germans built battlecruisers in the interwar years, not that it helped them, since I had a fairly good idea when the war was going to start, and parked outside of Kiel, and surfed the Med; the Japanese never concentrated their forces (enough), possibly because Yamamoto was looking across the Pacific, though seemed to think he could take New Guinea with two or three carriers and four or six battleships. Of course, I was waiting for him with all my battle, heavy and light cruisers; and four carriers. And twelve battleships.
At this point, you can switch production to light cruisers and destroyers.
Getting back to the paper part, it would seem in Traveller you end up in the Dreadnought era at tech level twelve. Battlecruisers and battleships will be built at the same weight, but they optimize characteristics most suited to fulfilling their roles.
Bearing in mind that armour strength is dependent on the material the hull is built with, armour plating takes up from seven and a half percent to ten percent, with the largest big ass meson gun available, that bypasses physical armour, meson guns being the torpedo analogue, whereas our torpedoes are just oversized missiles.
Normally, maximum speed and range would be a given, but with the range opening to nine gees, and possibly with a reaction turbo overdrive, so that engineering and bunkerage would take up fifty to sixty percent of volume.
Presumably, hundred thousand tonnes is still the limit at tech level twelve.
At tech level fourteen, the guys that wrote Fighting Ships of the Solomani got it correct, fast battleships predominate, and that's the end of the battlecruiser; though there might be a case for the improved armoured cruiser.
That leaves us with tech level thirteen, still stuck with crystaliron armour, the period you'd built an intermediate fast battleship, which would be the equivalent of the Admiral class, which could jump four parsecs, and ten percent of volume given to armour. That alone would be half of the ship, so the other half would be a compromise between armour, speed and firepower, and actual power. Of course, whether the designers would actually go for four parsecs, or stick with three is hard to tell, but assuming the rule is still for a single spinal mount, all that extra volume would allow for it.