Mirror image knots

I have recently become interested in the mirror images of knots. Many knotting books ignore the difference, and many knot tyers disregard the difference. I believe that there is a difference, as far as the strength or security is concerned, in many knots. According to CW Ashley, the mirror image of the sheet bend is less reliable than the regular sheet bend. To put it another way, a sheet bend tied using a left-laid rope is less reliable than a sheet bend tied using a right-laid rope. And what exactly does less reliable mean; less strong or less secure? The same would apply to the bowline. Has anyone any figures or a reference to show the difference? ???

Also according to CW Ashley, the left-hand sheet bend is less secure than the right-hand sheet bend, but has the same strength. Has anyone another reference to this fact? ???

The twist of a knot: ???
When making the timber hitch or the surgeons knot, for example, should the twist be right-handed or left-handed? I have seen references stating that they should be right-handed. However, when a right-handed Hawser-laid rope is made, the right-handed cable is made using 3 left-handed ropes, which in turn is made using 3 right-handed strands. This alternating opposite twist is to counteract the natural tendency to untwist. Does this therefore not imply that the twist of a knot in a right-handed rope should be left-handed?

Where have you come across Right Hand Laid ‘Cable Laid’ Rope?
As far as I am aware cable laid rope is always left hand laid, from three right hand laid hawser laid ropes.
There is a 6 strand right hand lay called ‘Lang-Lay’ but that is a wire laid up with the same lay as the strands.

Gordon