So, some more of my amateur maths:
Using my company formations posted above, I would be interested in targeting enemy ships with tonnages of 5k, 10k, 15k, 20k, 25k, and 30k tons, based on my scouting intel. Based on the crew numbers for my own ships, I come up with the following expectations for hostile crew numbers for each hostile ship size:
5k tons: 100-200 crew
10k tons: 300 - 400 crew
15k tons: 400 - 600 crew
20k tons: 600 - 800 crew
25k tons: 800 - 900 crew
30k tons: 900 - 1000 crew
I will now calculate how many of my boarding squadrons are required to capture ships of the tonnages listed above. These calculations assume the squadrons listed below have already survived boarding action:
5k ton ship: 4x Light Squadrons, 3x Medium Squadrons, or 5x Heavy Squadrons required to capture ship following completion of boarding action
10k ton ship: 10x Light, 8x Medium, or 15x Heavy
15k ton ship: 14x Light, 10x Medium, or 20x Heavy
20k ton ship: 20x Light, 15x Medium, or 30x Heavy
25k ton ship: 27x Light, 20x Medium, or 40x Heavy
30k ton ship: 30x Light, 23x Medium, or 45x Heavy
Finally, I will consider the impact of boarding action. A Jackson VII has a top speed of 21k km/s and the fastest NPR ship I have observed has a top speed of 7k km/s. So, the speed ratio is 21/7 = 3, and 3 * 0.2 = 0.6, so I have a boarding success rate of 60% for each boarding unit. So if I bring 2x as many boarding ships as my calculations above indicate that I need, I should be able to capture a target ship of each of the above sizes, accounting for the effects of boarding action. This is not terribly unreasonable given that each squadron is only 100 tons. I can fit 1x squadron on each Jackson VII and 3x Jackson VIIs on each Artemis. So now I will calculate how many fully loaded Artemis's should be adequate to capture a ship of each of the tonnages listed above:
5k ton ship: 9x Jackson VII on 3x Artemis III
10k ton ship: 21x Jackson VII on 7x Artemis III
15k ton ship: 30x Jackson VII on 10x Artemis III
20k ton ship: 42x Jackson VII on 14x Artemis III
25k ton ship: 54x Jackson VII on 18x Artemis III
30k ton ship: 60x Jackson VII on 20x Artemis III
Considering that each Artemis is accompanied by a compliment of particle beam and plasma carronade destroyers in equal numbers, I think these formations stand a chance at capturing some ships and that my fleet overall may be approaching a final workable configuration for my upcoming encounter with my local hostile NPR.