I'd vote for Eagle being available on the 11th
Primarily because its a smaller POD but also because it keeps the Taranto on its OTL schedule
the OTL Judgement was part of an overarching set of operations (MB8):
- 6 separate naval forces (in addition at least two met and exchanged components)
- Effectively 5 convoys (tho two held no merchantmen with skilled men and key supplies on fast warships)
- 1 cruiser raid (that sank 4 merchant men plus an escort)
- 2 separate carrier airstrikes - the sucker punch being Judgement itself
A CV was needed to cover the Western half of this waltz
including 'Crack' an air attack on airfields in Corsica
so although using the Ark - with more Swordfish than Lusty + a squadron of Skuas - is a temptation
Occams razors prefers the lesser change
Of course IF Eagle is fully operational, Judgement might have gone ahead 3 weeks earlier - Trafalgar Day would have been nice
I accept your points about the appreciation of dive bombers and larger number of a/c
but Eagle and Illustrious would also show the use of a large strike from a CV Task group
for an earlier date the deception plan would have been different and maybe the Ark could also have been used more fully
(I vaguely remember reading that prewar planning had consider a 3 CV strike any way using F,C & G ious)