I can get Latin Greeks down to 7BG:
IC, FC, 2xTC - 200AP
2x6 Kn, HArm, S, UD, L, Sw - 276AP
2x4 Kn, HArm, S, UD, L, Sw - 184AP
1x4 Kn, HArm, S, D, L, Sw - 104AP
2x6 LF, UnPro, P, UD, Bw - 36AP
For 6BG? Tried Medieval French, the AP numbers don't add up. Then I thought of Ordonnance:
FC, FC, 2xTC - 170AP
3x6 Kn, HArm, S, D, L, Sw - 468AP
1x6 MF, Pro, A, D, LBw, Sw - 54AP
1x6 MF, UnPro, P, UD, LBw - 24AP
1x4 Kn, HArm, A, D, L, Sw - 84AP
Now is 5BG even possible? I think I know of one





