Your knotted specimens have a ShakeHandsEsque appearance. Do you starch them, or pin them, to maintain their shape before photographing?
What I get is a knot which is not as neat, compact, nor as pretty as your images suggest.
Perhaps because you tie it in-the-end, and you have not tied it so many times to feel how much you should pull each string ?
Tie it in-the-bight, following the simple, straightforward method I had shown, and you will see that it takes the correct form much more easily.
No, I do not do any such magic trick !

I just DRESS it correctly. Knots, among other things, should be dressed ( or not ?

)
Can you tell me why I should choose your Plait Loop over the Farmers Loop for any task.
What advantage does P have over F?
Starting from a secondary, but still important feature, which is obvious to me, but I understand that it may be not so obvious to others :
The P has
a pattern - the only F s pattern is the shape of a farmer s , or a farmer cow s, you know what !

Knots that have a pattern, can me memorised and remembered more easily ( because the human mind works that way...), and, more importantly, can be
inspected more easily ! Any mistake would be like a fly in the ointment, because it will destroy the pattern of the plait, and will generate the pattern of the s... instead...
Now, the two loops are NOT meant to be loaded in the same way ! The P is an end-of-line loop, which is EEL : it can be loaded by the one, the other, or by both ends simultaneously. Those ends are parallel to the eyelegs ( almost - we are talking about the general case, where the loop is very elongated, i.e., not ring loaded ). The F is an in-line loop, which is meant to be tied in the middle of a more or less tensioned and straight main line, and support something hung within its loop.
See poor old Ashley : the man has put the in-line loops the one after the other in his chapter, although his general taxonomy throughout the book is, well,
Farmers s loop-like !

See how F s depicted, in all its drawings and its pictures : It is either loaded by one, only end ( and, in particular, the end which makes this odd fellow look as much less rickety as possible...), or by both ends, which, because of that, point to almost opposite directions.
You have to examine the F a little more carefully, and see that it is not symmetric regarding its two ends : it behaves differently, and it takes a different shape and orientation, if it is hung by the one or by the other end. ( the same happens with many of Ashley s in-line loops ). The continuations of the two Standing Ends inside the nub follow entirely different paths, they distribute the tensile forces entirely differently. On the contrary, the P is just
two interlinked crossing knots, the one above the other ! It is, and it "works" so, as a crossing knot-based end-of-line knot, independently of the Standing End from which it would be hung. It ia also not-symmetric, of course, but if you examine it a little you will see that the continuations of both Standing Ends follow almost identical, geometrically, paths, and, when they will be loaded, they will be loaded in almost the same way. The fact that the one crossing knot is "above" the other, or more near to the corresponding Standing End, and the other "below", more far from it, does not mean that they will behave differently.
With P, you have an easily inspected loop, which "works" in the same way when it is loaded by any of its two ends, and which way is transparent, easily understood and well known : all crossing-knot-based bowlines ( the "Eskimo" bowlines included ) work in this way. I tried to figure out a loop that is truly EEL, works (almost) in the same way when it is loaded by the one or the other end, and it is PET-2 - and P was the result. I had NOT tried to tie an in-line loop - because, to my view, we already have the great
Butterfly loop - and I had already tied such loops, as the
Sheepshank loop, for example (1). Please, notice that I call the
Sheepshank loop, as
loop, meaning an in-line loop, and not as a "bowline", because the
Sheepshank bowline, presented in the same thread, is clearly a different knot !
You may have been misled in this matter, because the
Butterfly loop is so stable, that retains its shape, more or less, when it is loaded / used as an in-line loop, and as an end-of-line loop. As you can see now, this is not the case with the P and the F, and the
Sheepshank loop and
bowline. The knots are very different geometrically, they "work" differently, I am SURE they will have different properties regarding slippage, strength and jamming - in short, they are different structures, and, to me, knots are structures, not shapes !
Also, as you may had noticed, the
Plait loop was meant to replace the
Pet loop, which is also a crossing knot-based TIB loop ( better, to my view, than the
Span loop ), but it is not very satisfactory as EEL, and it is not PET-2. One may see the
Plait loop as a "double" / "two-ends"
Pet loop (3).
Last, but not least : Do you ask ME about "applications" ?

As I have said time and again, I do not give a Farmer s s... for applications ! To me, the "purpose" of a knot is to remain "knotted" under load. Then, IFF and WHEN this is achieved, somebody, at some point of space and time, in this planet or elsewhere, may "use" this knot - but, most probably, I will not be around to see what will happen !

Enjoy an easily tied in-the-bight TIB loop ( we have many good TIB loops, which, unfortunately, can NOT be tied in-the bight easily - or we do not know how to tie them as such yet...), easily inspected, good looking from its "front" view (2), and almost symmetrically "working" if/when it is loaded by either end.
1.
http://igkt.net/sm/index.php?topic=46802.
http://igkt.net/sm/index.php?topic=5084.msg34751#msg34751