Blend Shapes not staying at 0 between animations

We’re having a problem with the animations that we’ve imported from Max. Specifically, it appears that some of the blend shapes (mesh targets) are not cleaning up after themselves once their associated animation is finished. For example, a particular animation might leave a particular BlendShape at 10, polluting all the following animations later on with its residual morphing. We’ve gone over these animations repeatedly and cannot figure out what distinguishes the well-behaving animations from the polluting ones. In case it's relevant, the animations are imported as Legacy and are played via Animation.Play or Animation.PlayQueued; no Mecanim involved.

Artist details: To set this up, we have a mouth mesh that has 5 different morph targets that can be used to change the mouth into different shapes of emotions. Animations will transfer from 0 to 100 and back as the animations play. Basically one animation will end at a certain keyframe pose, and the second animation will start from that ending keyframe pose to play the final outcome animation. The morph target from animation one is being carried over some how into animation two. Animation two still plays the morphing animation, but now has the added numbers from the first animation morph target ending. This creates a really ugly morph animation.

Is there some step in the animation setup, the export, or the import process that we’re missing. How do we make sure that the blend shapes clean up after themselves?

Cheers, BBD