As a very quick bit of work on Excel:
Theta: 20 Mechs, 6 Armour, 4 Infantry Level Is, 6 Fighters
Kappa: 18 Mechs, 4 Armour, 8 Infantry, 6 Fighters
Mu: 15 Mechs, 5 Armour, 10 Infantry, 6 Fighters
Combining 1 Theta, 1 Mu and 2 Kappa gives you short Level IV with about the percentage breakdown of Kappa.