perceptible jerks of the woodbox or the test objects
Yes, unfortunately I don't think that this is fixable, it would require smoother object handling by the engine.
objects sometimes "fall through" the floor or get stuck in the wall if they are compressed tightly by players
Same thing here, it would require engine changes. Realistically, the player could stand on top of objects and could not push them into walls, but unfortunately it is pretty much impossible to stop the player from moving. The player is basically unstoppable.
the rigidbody physics stops working correctly if it has a non-convex shape
Yes, this is correct. Non-convex shapes are incredibly difficult to get working, so the workaround here is to split up your non-convex shape into several convex shapes.