First, those three binders are NOT "based on the Clove hitch" ! There is nowhere something like a Clove hitch : the two aligned, separate nipping tubes ( which are connected only by the "bridge", and through which we pass the two tails of the hitch after they have wrapped the object ) are two double nipping loops : each double nipping loop is made by segments of the line that make one 540 degrees UUU turn ( = three 180 degrees U turns ). On the contrary, the Gleipnir Clove binders I had shown are based on one genuine Cove hitch, tied around the penetrating pair of ends.
Why a Clove hitch, and not just a double nipping loop ? I have seen that the Clove hitch behaves like a rope-made ratchet mechanism, "locking" any tensile forces which happen to be inserted within it during a pre-tensioning stage : so its gripping power on the penetrating tails is greater and more permanent, and will prohibit any slippage of the tails, even if/after they will become unloaded at some instance.
We can replace the two aligned, separate double nipping loops in those hitches, with two aligned, separate Clove hitches, and see what happens.
As you mention, we can place the nipping tubes as you show in the pictures, or upside down, so the "bridge" which connects the two nipping tubes is in contact to the surface of the object.
Now, we can insert each of the two ends that we want to "lock" inside the nipping tubes, through the one or through the other opening. It is true that, if we insert them "the other way" of the way you show, the two wraps will cross each other, so the binder/hitch will not be 100% "symmetrical" - but that is only a minor deviation from the 100% symmetrical way you show, a deviation which does not have any consequence in the efficiency of the knot - especially in the case of a mid-air binder.
I have seen that, curiously, the one, the "correct" way, can be quite easier to pre-tension than the other, and that is what I mentioned in Reply#32. ( See the two "ways", in the case of a "handcuff", one-line mid-air Gleipnir Clove binder, tied in between two objects, at the attached pictures. The same happens in the case of the two-line, mid-air or not, "common" binder / hitch, tied around one object. ) So, till now, we have four variations of the hitches you show.
Moreover, if we make the line to turn 360 degrees or 720 degrees ( = two 180 degrees U turns, or four 180 degrees U turns ), the two limbs of the nipping tubes will leave them, and will turn around the object, following opposite directions, so we have a new quadruplicating of the number of possible binders/hitches - although the form of the ones with the shorter or longer nipping tubes are a little different from the ones you show, and one would argue that, in those 4 "new" cases, we have something like two connected, through a "bridge", single or double, inverted or not, "simple-hitches-a-la-Gleipnir" in a row, aligned on the surface of the pole...
