So if I summarize my HR on BB,
BB A4D4M2C20 2 hits, can bombard 1@4, Plunging fire 1@1, no ASW, combined AA fire with cruisers.
Plunging fire: gain 1 additionnal A/D@1 against surface vessel DD, CA, CV, BB only (if present) on the opening round, it is not a surprise/first strike, so the casuality can return fire.
No ASW: attacking BB cannot hit any sub unit. When their is no other defending combat unit than Subs, she may stay in the battle to destroy any TTs remaining, BB destroy 2 TTs/round of battle. However, subs defends @1, and if their is no attacking DD with the BB, then Sub defense are Surprise/First Strike as OOB rule.
Combined AA fire with cruisers: paired with cruiser, each BB can give up to 2 cruisers 1 defensive and preemptive AA@1/cruiser against up to 1 AA roll/plane.
The cost is the same OOB.
I think, it is still balance since we reduce some offensive power against subs and, to counterweight it, give more specific offensive vs other vessel / and defensive capabilities vs planes in combine arms.
I made Plunging fire an almost regular strike at 1 on first round to keep it balance and, for historical reason, because even the poor HMS Hood was able to hit the Bismarck (which was the paradigma on which we base the plunging fire effect) and force it to return home for repair.
If someone wants the First Strike, keep it only for superbattleship (at higher cost).
It also have the effect of boosting DDs and CAs buying to protect them, gaining additionnal AA, and make Anti-Sub warfare.
From my limited historical point of view, it seems to better reflect their purpose in naval warfare.
Is it an interesting and enough historically grounded House Rule or not?
I should also add my revised HR for cruiser (for my next game):
CA A3D3M3C12 1 hit, can bombard 1@3, AA platform, combined AA fire with BB.
AA platform: any “1” hit must be allocated to 1 aircraft (owner’s choice) if present.
Combined AA fire with BB: when paired with BB up to 2 cruisers get 1AA@1 preemptive defensive fire.
As OOB, it can hit Subs on attack and defense but doesn’t block Surprise strike and all subs capacity.