Liesbeth Levick

If you don't mind the pieces being distorted, you can use a Muscle Deintersect SOP. Or, if you want the pieces to remain rigid, I set up a little example file that moves the pieces using the Detangle SOP as a starting point for calculating what direction to move each piece in.

The alternative is to use Bullet for the initial configuration, and then run the Vellum sim.

This isn't a scenario I've had a chance to test yet, so it would be very helpful if you could submit a file to support for me to look at. The Velocity Blend is designed more for helping the muscles to move with the bones and not lag behind them, so I don't know if that would help with overshoot. Have you tried the Velocity Damping setting on the Otis Solver itself under the Forces tab? Another option would be to try the "Constraints Only" damping method - but that would require changing all your damping values to be much higher - along the lines of what you'd use for Vellum for damping.

Do you want to move the pieces rigidly to resolve overlaps or can they be deformed?