Making the second stage reusable

A speculative post from a rank amateur.

Elon Musk wants to make all of his rockets reusable. But, as he said recently, it is really hard. If I may make a suggestion. Look at this picture of the Falcon 9 as it is being assembled for launch. Note the red ellipse that I've put into the picture.

Red ellipse marks where second stage fits on top of first stage.  Note the empty space where the nozzle fits.

Here's the idea.  Put another one of these empty spaces between the Dragon and the second stage.  After orbit is achieved, maneuver the second stage 180 degrees and slide it inside the empty space in a type of docking maneuver.

The empty space with be a heat shield that can withstand reentry.  It will probably need to be tapered somewhat as well.  The parachute will be facing in the proper direction, because it will be between the Dragon and the second stage before the maneuver.

After the maneuver, it will be facing "up"- towards space, and the nozzle will be facing "down"- towards Earth, with the heat shield protecting the engine.  The engine assembly will be the heaviest part, so it probably keep a proper orientation as it reenters the atmosphere.  Then you can deploy the chute and land gently in the ocean for retrieval.

If desired, the empty space can hold cargo, which go along with the Dragon.  That will require a separate docking maneuver with the Dragon, which will pull the cargo out, while leaving an empty space for the above maneuver for the second stage.


Update:

Why will this work? All the techniques and so forth are proven. It is just a matter of putting it together and trying.  Here are the reasons based upon what I've observed about the Falcon 9

1.  The second stage achieves stable orbit.  That's because it is used for the circularization burn that is necessary for every launch.
2. A heat shield for rentry would not weigh that much.
3. It could be fabricated out of a strong weight carrying metal such as titanium.  That is so it can hold the weight of the Dragon.
4. The docking maneuver takes place in a stable orbit and has been practiced for decades now.  This should pose no technical difficulty at all.
5. After the shield is in place, the rest is also old hat.  It would be very similar to recovering the Dragon itself.

And there you are.  I think it is a rather elegant and simple solution.  I bet that you that this may well be the way it is done before it all said and done.