For the sinking of the Dynamic into the Kinematic, I would suggest raising the values of these two properties which are located in the Nape.as class:
public var velocityIterations:uint = 8;
public var positionIterations:uint = 8;
I have personally experimented with as high as forty (both values do not have to be identical), this will lower the performance of the application, it may be noticeable, but depending on the application and the scale of the project, it may not cause an impact. Experiment with these values, the lower you can keep it, the faster your application will be, but the less accurate the physics simulation will become. Find the right balance that suits you. Instead of adjusting these values, you could set the isBullet property of both the bike and platform to true, which will enable continuous collisions for those objects, this will also cause a performance hit.
(Perhaps check the hit boxes again, to make sure they're a tight fit.)
Lowering the weight of the bike and increasing the weight of the platform may help, in achieving a trampoline effect. (I normally achieve this by modifying: <body>.gravMass = <Float>, perhaps there are better ways to affect weight, as I believe the calculation of mass initially depends on whether the body is a part of a compound and the size of the hit boxes given to all of the polygons which make up a body)
It might be worth trying a behind-the-scenes trick, in which you could artificially set the velocity of the bike when the angle of the platform exceeds a given threshold.
Watching the video back, I think the Kinematic platform needs to have a very aggressive velocity to achieve the result you want.
Could also experiment with the gravity of the entire Nape world via:<napeinstance>.gravity(<Vec2>)
Could also have an object attached to the end of the platform, if you want to maintain the slow acceleration of the rotation, which would be programmed to propel the bike into the air.