When demoing my project to Dr. Badler, he offered the suggestion of correcting the motions when the center of mass of the character changes significantly after creating an overlay. For example, if the character is running fast, he is naturally leaning forward. If you want to transplant an upper body motion on to this and use spatial alignment, the character will be leaning forward too much for it to look natural or even possible. We can use our physics checks to determine the character's center of mass throughout a motion. By comparing how the center of mass position changes in the upper body motion before and after transplanting it to the lower body motion, I can identify whether the character will be leaning forward too much or leaning back too much. If the change is enough that the character will need to slow down to maintain a close enough center of mass to before the transplant, I interpolate the lower body motion with a slower speed motion. Here is an example of what an overlay looks like before and after the speed is corrected based on the change in center of mass:
This is an admittedly rough implementation more useful as an example. I think this would be especially useful in games if the player wants to perform an action, but the character needs to change speeds automatically to perform that action properly.
Updated Note: For my presentation, I switched the way I did spatial alignment to align the lower body motion to the upper body motion. However, the approach I took initially is better I think (aligning upper body motion to lower body motion). As a result, the example I used in the presentation is the opposite of what is here, but I think the approach here is the correct one.