'Desyncing' multiple instances of Mecanim animations?

If I spawn several Mecanim-controlled characters at the same time, and same state/speed, their walk anims are perfectly in sync. I want to avoid this, for a more natural look.

Is there any way to programatically set the current playback time within an animation state, so I can make them start at a random point in their walk cycles?

I suspect the answer is no, as that seems to be the answer to most questions about controlling Mecanim via script, sadly - but maybe I've missed something?

(There's got to be a better option than excessive numbers of transitions and boolean parameters, something which is already giving me grief for characters that need to spawn in a number of different states...)