Why is a canard configuration more Structurally efficient for Rutan's Voyager? Firstly, I’d like to kindly request not to mark this question as a duplicate of previous SE question without first reading this, because the approach is different and the previously given answers are merely incorrect. 

Background

I found this information in VoyagerEssay.pdf from Burt Rutans website.

EDIT: I am putting this possibly redundant info with the hope it might help better clarify the problem as suggested. 

From Burt's own notes. 


  The range of an aircraft is determined by three basic criteria: its
  propulsion efficiency, its weight and its aerodynamic efficiency. I
  had to make major improvements in one or more of these areas in order
  to build an aircraft that could fly more than twice as far as any
  previous flight.


Please see "breguet-range-equation" for more info. And this range equation suggests us the range of an airplane is exponentially sensitive to the initial and final weight ratios; and linearly sensitive to L/D and total propulsive efficiency eta. 

And as the per the same source, this configuration was chosen to achieve higher structural efficiency.


  The primary reason we were able to double the old record related to
  our success in weight control. By using a new, unusual configuration
  we could place a large amount of fuel at three span-wise locations:
  the fuselage and two large booms at 30% of the distance out to the
  wing-tips. A very light main wing and canard wing provided just the
  amount of structural support for this large fuel mass. The two wings
  supported the fuel-laden booms via their bending stiffness without
  depending on the torsional stiffness of a single slender wing. This
  was Voyager’s secret to success. Its graphite composite structure
  weighed only nine percent of the take-off weight. The fuel consisted
  of 73% of the take-off weight. This phenomenal weight performance was
  the main reason we were able to achieve our goal of true global range.


And of course in return traded off aerodynamic efficiency.


  Regarding aerodynamic efficiency, I was unable to achieve a result as
  high as a typical sailplane since I was forced to use the unusual
  configuration


In this John Roncz presentation, he mentioned this configuration was to solve the problems of having high inertia fuel booms, [~18 mins] but without any specific note on how it resolves into a canard.
As per Mr. Roncz, he appears to suggest this minimizes the bending stresses of the booms. (Please correct me if Im wrong) and note from Burt appear to suggest the config was selected to minimize wing torsional loads. 

Question 

Can any of you please provide me with an explanation as to why the canard configuration ideally could be more beneficial for this design? 

My argument is if he had chosen the second config shown below, he would have gained BOTH structural benefits of canard plus aerodynamic benefits of conventional config.

 

In my eyes, this is an even better win-win solution but most certainly too good to be true; hence my question. 

If possible I would love to see some quantitative answer rather than qualitative but any constructive answer is more than very welcome.
I listened to John Roncz explanation more than a couple of times and figured the reason he was explaining. 

The first thing to understand is any aerodynamic surface placed in front of the CG is a DE-stabilizer. The aft wing is the stabilizing surface.

The high inertia of the fuel filled booms demand either a very torsionally stiff wing structure or else a very big stabilizing power characterized by higher tail volume. But torsional strength is very expensive in terms of wing weight because higher torsional loads imply a bigger secondary spar and thicker wing skins. 

Considering the fact that the Breguet range equation favors higher structural efficiency over the other parameters, It appears that Burt chose the second approach. This adds to the second benefit that wing and canard both subjects almost only to the bending loads. 

Quick number-crunching shows that with 10% static margin canard configuration leads to ~7 Times statically stable airplane than the conventionally configured one.



EDIT:
As of why GlobalFlyer with very similar mission requirements used conventional configuration could be tracked down to the following reasons. 


Due to the nature of the Voyager project, Burt's responsibility was only to design the airplane. The materialization of the design was on Dick and Jeana, he opted for the most simple structural solution with the minimal analysis he could come up with at the time. 
As per the previous analysis on tail volume comparison, it is clear that conventional configuration provides only minimal "P" gain for the longitudinal transfer function; meaning that dampening out a gust response, for example, could result in diverging oscillations or even a stall. At the time, I believe completely failsafe autopilot is not a feasible solution given the additional weight it put and/or risks it brings onboard. 
Also, Global Flyer demands even a higher fuel fraction due to fuel thirst jet engines, so losing the aerodynamic benefits of conventional configuration was not a feasible one. Instead, they ended up utilizing a fulltime autopilot.