How does Unity handle interpolation between keyframes in animation? Our model in 3DS linearly interpolates (as it should), but in the game it seems to “bounce” past where it’s supposed to go.
I’m not sure if things are different when importing animation from Max (I’ve only used maya with Unity) but a good way to ensure that your animation curves don’t get messed with is to go to the import options for that asset and click the checkbox to bake the curves on import. Without baking the curves, Unity sometimes does some silly things like what you just described.
I don’t see that option in the import… 
Right click the asset, choose Import settings, and turn off keyframe reduction (and turn on bake IK and simulation if possible) and see if that helps. If not, you can always bake your curves animation out in Max I assume.