The speed of the German task force (again limiting it to the Bismark/Tirpitz, the Scharnhorst class, and the Hipper class cruisers and Graf Zeppelin) is extremely fast (something on the order of 31 knots) Eagle wouldn't really be helpful in that scenario
That leaves Ark Royal and Furious; which are fast enough to keep pace with the Germans. They would need to join up because either one individually is not enough likely overwhelm the Zeppelin which I assume would be the highest priority target
The battleships is something I've never really considered... only Hood and the Repulse/Renown could keep pace with the German fleet; and they are poorly armored to withstand a gunnery duel with the Bismark and Tirpitz; provided the Germans could keep their air cover alive, and not run across any British submarines, they could pick and choose their engagements, trying to attack lightly escorted convoys/force scatter; or run from the British home fleet whenever identified
The British are limited to the low speed of the Nelson class because they cannot win a surface engagement without them
Zeppelin had a very low sortie rate as it used a pneumatic catapult which took ages to cycle.