I came late, but am enjoying this TL. Regardless of whether or not some earlier POD is required (probably is), this is an attempt to mitigate one of the problems.
I would like to offer a few perspectives.
First, from the beginning the RN recognized that their greatest difficulty would be establishing Air and Sea Control around the Falklands. They established Sea Control pretty quickly, in part aided by the dysfunctionality of the Argentine submarine force; and HMS Conqueror sent the fleet home for the duration when she sunk the Belgrano.
So, when considering a mission-specific air group for HMS Eagle, the best use of limited space is air defense (including AEW) and ASW. The Buccaneer does not bring a "missing" capability to the party in light of Harrier availability. The AN/APS-20 is very limited, but better than the alternative (i.e., nothing), so the Gannett is necessary. While the Buccaneer would improve ground strike capability, I would only take a few along if believed necessary to counter the Argentine surface fleet. However, the SSNs would make that a low priority in my estimation.
Ponder this view of HMS Ark Royal.
View attachment 399952
Not much room for a deck park without locking the flight deck. However, when running CAP operations, first glance looks like one could spot 6 Phantoms on deck without blocking the waist cat (which is the only one capable of launching a Phantom) or landing strip. Lacking a tanker capability, the cycles are probably going to be fairly short, perhaps 1 + 30 (90 minutes) as a guess (want to maintain a good amount of combat fuel since the fighters will need to engage multiple targets when the enemy comes). That's really not too bad since the Argentines don't really pose a night threat. So, roughly 10 hours of flight ops per day (8 hours + twilight), and one can subtract flight time from the Argentine air bases from the CAP period. So, possibly 6 cycles per day??
A squadron of 12 (if they maintain 100% mission readiness) could sustain a 4-aircraft CAP, and 4 on alert-5. Some of the enemy strikes (early on) were in the 30-aircraft range, so that is probably an absolute minimum package. Really, 16-20 mission capable aircraft is much better. Hitting the attackers hard in the early phases would probably have a very positive impact (pour encourager les autres) - perhaps 4 up and 6 on alert-5 sends the proper message. For the sake of argument, let's assume the squadron personnel can accomplish their maintenance time during the night.
If it was up to me I would put 20 x Phantom, 5 x Gannett AEW and as many Sea Kings as I could fit on the HMS Eagle. Any Sea King not flying an ASW mission can assist with logistical and operational lift requirements. No room for the Buccaneer without compromising air defense.
IMHO that argues for cramming every Phantom possible onto HMS Eagle. Relative to carrying the Buccaneer, also remember that the Phantom is a very capable strike fighter. If the enemy launches two strikes per day and each strike is met with 10 aircraft, that gets you in the range of 36 fighter sorties per day. Add another 5 x AEW and 20-24 ASW sorties and I am guessing one is at or above the maximum sustainable sortie rate for a carrier this size.
I would offer that the presence of HMS Eagle allows one to replace the Harrier GR.3 squadron on HMS Hermes with helicopters. Keep the 28 Sea Harriers deployed on Hermes and Invincible to augment the AAW package (between the Phantom CAP envelope and the close-in missiles) and provide CAS. Now one can employ four "real" layers to the air defense - Phantom CAP - Sea Dart - Sea Harrier - short range missiles. Even if the AN/APS-20 only extends the detection range by 50-75nm past the Type 42 detection range, that could be very significant. The Argentines were not flying at wave height, so maybe even 100nm extra detection range? Perhaps Sheffield and Coventry survive as well.
Logistics for the ground force was the second major issue throughout the campaign. Improved ITTL if Atlantic Conveyor does not go down, but still insufficient. During OTL the lack of amphibious ships and landing craft resulted in a plan to use "sea-based logistics" (SBL) for part of the package (a pretty wild dream considering the available capabilities). In any event, SBL requires more helicopter support than the fleet can carry. Loss of the Chinooks on Atlantic Conveyor is often cited as creating the deficiency, but that really just made a bad situation worse. The USMC/USN has "played" with the idea of SBL in combination with STOM (ship-to-objective maneuver) for years, but many studies establish that the number of helicopters, MV-22s, etc. available is not sufficient to meet operational and logistical needs.
The ground troops had to "yomp" significant distances, and four more Chinooks would not have fixed the problem. There never were enough helicopters to handle either ship-to-shore or operational requirements, let alone both. What the British ground troops accomplished without adequate mobility and logistical support is simply amazing IMO.
I would also caution against attributing the "published" Harrier capabilities to performance in a ship-borne role. The ski jump increases the maximum takeoff weight by ~1,000lb over a straight deck run, but the published Harrier load and range capabilities are based on 1,200' to 1,500' takeoff runs from the ground. The maximum takeoff weight from a carrier is significantly less than from the ground, meaning less fuel, ordnance and endurance. IIRC, the Sea Harriers had an ~90 minute total endurance in AAW configuration during the Falklands campaign. This severely limited their CAP operations, especially considering the forced standoff range from their launch position east of the Falklands. Don't contribute the skill of the pilots and the Argentine Air Force limitations to some "significant" AAW capability for the aircraft. An extraordinary performance by the pilots and their squadron mates (keeping them in the air) with an aircraft that has very limited capability from a "carrier" deck. An engagement within range of enemy fighter support would be very, very dangerous for an STOVL carrier equipped with Harriers.
The statement to the effect that "another six properly functioning bomb fuses" could have changed the outcome is not really hyperbole. The "Phantomized" HMS Eagle would completely alter the equation.
.
Screenshot (5) by Frank Judge, on Flickr
C2ERQR-XgAEx8ts