Hoplophile,
You're correct about Kali including right angle weapons like axes and hawks. An instructor from the Philippines showed me some axe/hawk techniques he had learned there. Guro Dan Inosanto also has some material for axe/hawk. He said that a few of the older native-born Filipinos would hold the hawk in reverse grip (hand near the head, shaft coming out of the top of your hand, edge facing forward just below your hand). They would use the shaft for Eskrima-type stick work and the blade for close fighting. I played with it a little but decided I'd want a shaft closer to the typical 24-30" Eskrima stick, rather than the usual 14-18" hawk shaft.