The alpha strike rules handle capital scale much better then classic rules do. Like, I have done a few naval games, and we straight up played it incorrectly. The actual way you are supposed to resolve stuff, with the capital damage divisors and SI divisors and all, and lots and lots of hit rolls fishing for 12s for crits, is very different from what I remember playing back when I first cracked open my battlespace box set. It wasnt until the bot in megamek could do aero that I saw how things 'should' look, and was able to play more games of battlespace.
Capital squadron fighters makes things simpler, but also massively boosts the power level of fighters. Capital fighters being so much stronger in classic then normal fighters was such a shock to me, I put up a post on the forums about it. I dont think its a great way to handle aerospace and warships together.
The alpha strike rules already divide damage by 10, so are much better at integrating the capital scale stuff. It simplifies the crazy bays and locations and such to the point of 2 warships clashing being a quick decisive affair, allowing you to play with more then 1 warship. The Mckenna, for example, has a broadside of 261 at long range, 443 armor 95 structure, and a threshold of 37. Resolving an attack is one hit roll, 1 crit roll. Now, in classic, the same mckenna in the side has 4 FLS, 3 broadside, 3 RLS, so there is fiddling with lining up weapons more (but in the end all 3 bays do line up, so its not like having 8 firing arcs is that useful), and resolving the attacks is 6-10 rolls, with the same amount of crit rolls. And the mckenna is one of the simpler ships, as it doesnt have as many bays of standard weapons as many newer ships like a Thera with 7 FLS weapons bays, 2 point defense bays, and a capital missile bay in just the first of 3 side locations.
The only issue with the alpha strike rules I have for playing is that I really want better squadron rules. Battleforce has squadron rules, and fits the scope of a warship fleet v warship fleet action, but doesnt have as much support. Even the alpha strike rules cards for warships is not current, but I do believe the alpha strike warship cards are the most recent printing of warship specific 'things' we have had right?
I posited a 'space battle matched play' mission type of alpha strike a while back. For a 2000 point alpha strike level space game I settled on 0-4 squadrons of fighters/small craft, 3-6 squadrons of dropships, and 0-1 warship squadrons for the 'base level' game. The squadron rules were the simple battleforce ones, where every unit can be selected to be shot, but I made some suggestions such as units must be identical within squadrons + damage rollover, to make record keeping easier. By forcing the squadrons in such a way, you only end up with 10-11 maneuver elements max, which for alpha strike feels about right. So if you go fighter heavy, well its still just 4 maneuver elements of fighters, you just have bigger stacks of fighters (and thus smaller stacks of dropships, or no warship, ect).
The basic mission was attacker/defender, where if you were the attacker you scored points for delivering cargo to the target hex (probably a planet), 1 point per mech or 1k tons listed as ck# on the aerospace cards. The defender gets 1 point for every point of transport they destroy. In pitched battles, both sides are trying to destroy each others cargo to win the attrition/resource war (no planet to deposit cargo in that mission), and in relief missions both sides are trying to get cargo to a planet/hex, the side who puts the most cargo on the planet winning.
Anyway, thats the aerospace game on the table that I play nowadays/am willing to play. All alpha strike, set limits on maneuver elements to prevent the 'unit activation bloat', and only 0-1 kind of warship in the base game size of 2000 PV. With my missions being cargo mission objectives, the 'escort' warship is valuable, as getting that many ktons of cargo above a planet is a lot of points, and likewise LOSING the warship is a massive blow to the victory points. The clan vincent 42, for example, is 92 ktons of transport, so if a vincent gets in orbit of an enemy planet it earns the attacker a lot of points, compared to a mule at 8 ktons of cargo--but again, LOSING the vincent is likewise a massive blow, making the escort warships exciting centerpieces at my scale in alpha strike. The gametype was built so that you dont need the big warships at all, representing a 'normal' naval engagement. I posted sample fleets somewhere, but the 'basic' inner sphere fleet was like a squadron of Leopard CVs, a titan, some avengers, and the mission critical point getters were dropship groups--mules and unions. 4 aerospace stacks. The clan counterpart was a vincent, with 3 dropship groups and fighter stacks. Fighters still tend to be the focus, but by hard forcing them into 4 groups they dont make the rest of the game unplayable at 2k points, and with damage roll over in squadrons its not a massive painful grind. Without hard forcing fighters into 4 stacks, the fighter squadrons are just so many maneuver elements that the game was unplayable on the tabletop. The recommended squadron sizes were just woefully too small, leading to my '4 stack' limit for the smallest 2k games.
If you dont want to use the alpha strike rules, then honestly good luck. 1 Warship v Warship is fine, but you kinda have to bend over backwards making excuses for not using the 50+ fighters/dropships many warships just come with. And if you do use the integrated support stuff that comes with warships, then those elements almost instantly take over the majority of the game time. Even in squadrons of 6, the 10 squadrons you get out of 1 mckenna makes a 'mckenna versus mckenna' fight instantly take 10x or more time to resolve in classic rules, and the capital fighters rules make said fighters super deadly, which quickly undercuts the warship v warship action.