Before I could make the ragdolls match animations, I had to make them match poses. To test this out, I just made them hold their current pose when I press the 'ragdoll' button. Here's a video I took while testing this out:
Be sure to watch it in HD!
To create the 'frozen' effect I just add an extra constraint at each joint with the desired relative orientation of the affected bones (which is calculated from the animation pose). I then adjust the constraint-force-matching and error-reduction-parameter values to choose how rigid or flexible the frozen joints should be.
Do you have any questions about how it works, or ideas about what I should do with this technique?