Hi Marco,
You might know my standard answer, I think Dynamic is great, but sometimes not a one button solution. I like control—but I know as well that Dynamic can produce some movements much more believable. The key is to know when to use which one or when to mix.
However, having said that. I see three steps. Box shakes (1), settles down (2) and a new jumps out (3). If I got it right, it repeats—Matryoshka.
(1+2) Three is no need to have in that state the Lit and Box separated, it can be one. Perhaps, you might use Cappucino to turn it into a Keyframe animation to that point, for that time frame.
(3) is the part where the model is tricky. The Dynamics setting in the Project Setting might be adjusted to a higher solving-setting(Steps/Iteration)
I have attached a scene file that handles the critical part. (Cube = Lit) Even in reality—do you get such a lit easy off the box? I don’t, except when I use both hands. The lit needs to be guided for that short moment. If that short distance is done, “we” release the guidance and everything will go its way. You might capture that (Cappucino perhaps), and add some wiggling to the guided part. Which means to wiggle to box as well a bit. Great when you have keyframes then. ;o)
Please keep in mind that you can always place a “proxy” object instead of the the “visible” object in the scene. With more distance, but with a different “Size Increment” (Rigid Tag)
I hope that helps to get it done.
Have a good one
Sassi