Since I found my first Outlaws earlier today, I will now have to play it soon as well...
Since I'm not prepared to waste your amount of soldiers, LordFrancis, I had to recalculate at least the first 6 camps for minimal R losses...
These are all simulated at least 500 times, to give the biggest minimal losses you could encounter, in accordance with Sid's practice.
1 - 100R 1S 75C 24LB (100R)
2 - 43R 1S 125C 31LB (43R)
3 - 85R 1S 100C 14LB (85R)
4 - 1: 70R 2: 67R 1S 125C 7LB (137R)
5 - 1: 120R 2: 120R 1S 79LB (240R)
6 - 1: 95R 2: 29R 1S 160C 10LB (124R)
Note the two waves on camp 6, first wave to take out the dogs, then you can use cavalry in the second wave.
Also, rather than using your bowmen on camp 15, you can use bowmen instead of recruits (or a combination of them) in the first waves on camps 4 and 5:
4 - 1: 65B 2: 67R 1S 125C 7LB (67R 65B)
5 - 1: 114B 2: 120R 1S 79LB (120R 114B)