I think the simple and obvious way to do that is to reduce navy cap rather than add more limits to battleship numbers (especially since BB fleets are more performant then non-BB fleets because they're smaller).
See, the cap is really more of a
suggestion rather than a ... cap. So, sure, shrinking it helps - but you're also shrinking it for the other side too, so this definitely makes the game faster - but with respect to alpha strikes specifically, relatively speaking, changing the net-cap on it's own does nothing. Fewer L-guns firing at fewer targets leads to the same outcome - more or less.
The AI does not (ever?) exceed its naval cap, only players do - aggressively so if you have a strong economy (easy in 3.0+ with all the edicts and power creep from output multipliers). Setting hard-caps on the 4 classes does solve this, with the option (I'm still trying to figure out) to run an edict to inflate the caps, at risk of making anyone else in the GC, that isn't friendly, mark you for sanctions.
so, right now i've got it set up like this.
Class | base (non- mil/pac/ Gestalt | pacifist | F.pacifist | militarist | F.militarist | Gestalt | Exterminator civic |
Corvette | 100% FP | 100% FP | 100% FP | 110% FP | 130% FP | 115% FP | uncapped (vanilla) |
Destroyer | 90% FP | 80% FP | 60% FP | 100% FP | 120% FP | 105% FP | uncapped (vanilla) |
Cruiser | 60% FP | 50% FP | 30% FP | 70% FP | 90% FP | 80% FP | uncapped (vanilla) |
Battleship | 30% FP | 20% FP | 00% FP | 40% FP | 60% FP | 50% FP | uncapped (vanilla) |
So for example, only 20% of a pacifist's total fleet capacity can go towards battleships, and fanatic pacifists can build
no battleships at all. Whilst militarists can build more of each ship class than most nations. Now, by setting caps like this, you can
also encourage the AI to "top-fill" their navies, by weighting BBs with a high chance for construction in the games files, and once that's maxed, CVs follow, down to DDs etc.
And still looking at adding a perpetual Edict for non-exterminators that can slap an extra 25% on to all 4 class limits (so a fanatic militarist running this could get up to 85% of their fleet made out of BBs). But can be used to flag you in the GC for sanctions.
This also means when you hit your cap (unless you are in a category that has >100% FP for a ship class, or using the above edict, you cannot exceed your naval capacity at all, the game bars more of those ships being built). I did think about re-balancing the percentages as techs unlock (so when you unlock DDs, CVs falls to 80%) but it was leading to some weird errors, so always letting you build all corvettes is a simple enough compromise.
I've been too busy with other things to test this thoroughly, but it was interesting seeing pacifists fielding radically different fleets to militarists, not in %Armor/Shields or kin/Eng/Missile but in actual ship classes/fleet compositions.
Haven't gotten around to touching federal fleets, so they're probably uncapped for now - but could inherit caps based on the kind of federation using them (e.g. military-alliance federal fleets get more BBs than a galactic union or a trade union).
And the Custodian / Imperial fleet ratio could also be FP-weighted, with new resolutions to increase or skew the CV/BB limit - at the cost of,
ahem, higher taxes for members (and perhaps more calls to dissolve the custodian / oppose the imperium - as they become more oppressive/powerful).