Mat, I’m afraid to say it but, you’re wrong on all fronts.
Using a battle simulator I have I got the following results:
10000 trials to smooth out randomness, rounding errors may cause sum to exceed 100
Scenario #1 Defender has 6 DD, 0 BB Win | Lose | Mutual destruction
A) Attacker has 3 BB, 0 DD 32/62/6
B) Attacker has 2 BB, 2 DD 40/54/6
C) Attacker has 1 BB, 4 DD 44/50/6
D) Attacker has 0 BB, 6 DD 47/48/5
Scenario #2 Defender has 4 DD, 1 BB
A) Attacker has 3 BB, 0 DD 33/59/9
B) Attacker has 2 BB, 2 DD 41/51/7
C) Attacker has 1 BB, 4 DD 46/47/7
D) Attacker has 0 BB, 6 DD 50/44/6
Scenario #3 Defender has 2 DD, 2 BB
A) Attacker has 3 BB, 0 DD 36/56/9
B) Attacker has 2 BB, 2 DD 46/46/8
C) Attacker has 1 BB, 4 DD 52/41/7
D) Attacker has 0 BB, 6 DD 54/41/6
Scenario #4 Defender has 0 DD, 3 BB
A) Attacker has 3 BB, 0 DD 45/45/10
B) Attacker has 2 BB, 2 DD 57/35/9
C) Attacker has 1 BB, 4 DD 60/32/8
D) Attacker has 0 BB, 6 DD 62/33/5
Since a fully loaded carrier, DD and BB costs 78 IPC or 8.333% more than 6 destroyers you are not comparing apples to oranges. Since 6 DDs defend or attack at 18 lets add 8.333% to this. Since that is 1.5 I will round it down to just 1 more attack or defense. I should have 8.3% more units, since I cannot represent a 1/2 unit I will round down, this will mean the results should be a bit better for the destroyer side then the numbers will show on 2 accounts. The extra 1 offense/defense will be represented by increasing the offense and defense of a single destroyer to 4 and obviously take this unit off last.
6 DDs attacking 1 DD, 1 BB, 1 CV and 2 FTRs results in 46/46/8 result
1 DD, 1 BB, 1 CV and 2 FTRs versus 6 DDs results in 29/65/6 result.
It clearly shows a trend in advantagous occurances as you move towards 6 destroyers from 3 battleships.
Even with your mixed fleet, destroyers come out as the clear winner. If you already have fighters, then building enough carriers to hold them is the best bet for fleet defense, so the US should build 1-2 carriers. A mixed fleet also has the advantage that fighters can be used on land better than destroyers. However, the excercise was limited in scope so you will have to weigh pros/cons as the strategy dictates.
BB