Hydrogen Bonding in Water Phase Changes How is the disparity between the heat of fusion and the heat of vaporization for $\ce{H2O}$ best explained?

A) It takes more hydrogen bonds for water to fuse than it does to vaporize.

B) Water molecules are moving farther apart during fusion than during vaporization.

C) Water molecules are moving closer together during fusion and farther apart during vaporization.

D) Vaporization occurs at a higher kinetic energy than fusion.

E) More hydrogen bonds are broken during vaporization.

At first, I tried this problem via Process of Elimination. I looked at (B) and immediately knew that that fact was false, because water molecules move closer together during fusion, and farther during vaporization. Next, I saw (C), and though it was true, it had no involvement with the problem. (How far the water molecules move does not have anything with the disparity between heat of fusion and heat of vaporization). Then, I saw (D), and though it was also true (vaporization occurs at a higher temperature than fusion, and kinetic energy is directly proportional to temperature), I felt that it did not relate to the problem. So I have ruled out 3 of the 5 answers by now. It was the options (A) and (E) that stumped me. I did not know the relationship between the temperature and Hydrogen bonds in water, and conducted some research on the internet.

I found a useful link http://www1.lsbu.ac.uk/water/water_hydrogen_bonding.html , and saw that answer choice (A) is in fact true, if you look at the graph towards the end of the page. It has more hydrogen bonds in the solid state than in the vapor/gas state. So, I thought the answer was (A). However, I looked in the answer key provided with this question, and the answer was (E): more hydrogen bonds are broken during vaporization. I don't really see how this is, and would like assistance and answers why. Also, I would greatly appreciate an explanation for why the number of bonds increases when temperature is low, and decreases when temperature is higher. Even an explanation on how hydrogen bond numbers (approximately) change as phase changes would be great.
The molar heat of fusion for water is 6.02 kJ/mol (http://www.chemteam.info/Thermochem/Molar-Heat-Fusion.html), while the molar heat of vaporization for water is 40.7 kJ/mol (http://www.chemteam.info/Thermochem/Molar-Heat-Vaporization.html). That is equal to 6 times difference, even a little more. I suggest this energy is used to break existing hydrogen bonds and barely for anything else. The energy of hydrogen bonds is "6-30 kJ/mol" according to this source: http://book.bionumbers.org/what-is-the-energy-of-a-hydrogen-bond/.
Let's consider for simplicity, that breaking 1 mole of hydrogen bonds will require 6.02kJ of energy.
So, when water melts, there is maximum one mole of hydrogen bonds is broken per one mole of water. That is totally different for vaporization process: during vaporization of 1 mole of water it looks like 6 moles of hydrogen bonds are broken.
This invariably leads one to answer E:
More hydrogen bonds are broken during vaporization.