My take on the whole 'free will' issue with inhuman characters is that if it quacks like a duck and walks like a duck and floats and flies then even if its not a duck its close enough to count.
When we talk about free will vs being a monster its not a question of does it have a soul, but rather does it behave as though it does. A serial killer who can't resist killing is a monster, has a negative refresh and isn't a playable character, but he has a soul. It could be argued that both Bob and Toot, could be considered as having free will because the both demonstrated the ability to act outside their station or to become something greater then their design.
Bob does all sorts of actions that look as though they are free will, he takes mister to a strip club and a frat house, he tries to kill his owner when he's evil, he makes a dinosaur eat someone he doesn't like. He's still tightly bound to his supernatural constraints but he constantly shows he's got wiggle room, like maybe 1 refresh worth of wiggle room. Toot consistently acts beyond his station, he killed a faerie queen, attacked shagnasty and organized a fighting force, none of which is part of being a tiny pizza loving dew drop faerie. It could be argued that it was dresden's actions that lead them to all that but the same could be said about Lash's act of free will too.
They might not have free will but they sure act like it. And just like the serial killer is a monster, maybe these soulless beings have free will. Freedom isn't always a black or white, sometimes is a matter of degrees, and a character just has to be free enough to go above and beyond the call of compels to be free enough to play. If you're looking to have a construct as a character look to these for the Dresden lore surrounding free will and then look to Pinocchio and Dorothy's wizard of Oz companions for creative inspiration. Maybe your golem who wishes he had free will has had it all along. YMMV