The answer to your question lies in the structure of the polymer backbone structure and how that allows the polymer chains to pack.
HDPE is essentially very, very long chains of -CH2- groups:
-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-
These chains can lie very nicely alongside each other, like the threads in a length of rope. That allows for significant sections of crystallinity, because large portions of these chains can pack together into linear crystal structures. The term "high-density" comes directly from this ability to pack close together, as compared to "low-density" polyethylene, in which the chains are more highly branched. Each branch interrupts the crystal packing.
As for PVC, it is the same thing except that every other carbon has a bond to a chlorine atom instead of one of the hydrogens in HDPE:
Cl Cl Cl Cl
/ / / /
-CH-CH2-CH-CH2-CH-CH2-CH-
These strands can't pack as tightly together because the chlorine atoms get in the way. That lowers the crystallinity of the material, and makes the resulting structure more amorphous.
In terms of the physical properties you refer to in 2) of your post - the better backing ability of HDPE increases the areas of crystallinity, which increases the glass transition temperature - it takes more energy to convince the chains to move past each other and form a more disordered, amorphous mix. There are no crosslinks in either of these polymers (unless other monomers are added to give crosslinking points).
There are applications where more crystallinity for the polymers is desirable - in general, the more crystalline a polymer is, the harder and more brittle it will be. This allows it to withstand wear better, but can make it weaker to impacts. Amorphous polymers tend to be more flexible, but more malleable and more durable. For your application, my guess is that you are looking for a flexible, durable, tough material, rather than a harder, stiffer, more brittle material.
Hope this helps...