... At this point it all seems like voodoo to me.
Edy, before digging down into UnUns, BalUns and other antenna ideas, I believe you may use what you already have and try putting together an antenna; in your case, the NooElec 9:1 (or clone) will fit, start by looking at its schematic (which hopefully will be the same even if you have a clone and not the original thing)

now, if you cut that "0 Ohm" resistor marked R1 in the schematic (it's on the back of the board) you'll obtain a 9:1 transformer just
like the one used by KK5JY for his loops, at this point it would be easy putting up a simple wire loop (see
my other post, please) and testing it.
As for the impedance transformation ratio, the "square rule" is correct; if you look at the KK5JY transformer you'll see that we have two turns on a side and 6 turns on the other, now if we divide 6 by 2 we obtain 3 and 3^2 will give us 9, which is the impedance transformation ratio; in the case of the UnUn, let's say we have a trifilar winding made with 4 turns and connected (in series) as an "autotransformer", now, in this case we consider the number of turns for the primary (4) and the total number of turns for all windings (12) and if we divide 12 by 4 we obtain 3 and, again, 3^2 gives us 9, that is the transformation ratio
Let me make another example, let's say we want a 16:1 UnUn, we wind it quadrifilar (4 wires) and make 9 turns, the total number of turns will now be 36, and the primary will have 9 turns, now, if we divide 36 by 9 we obtain 4 and 4^2 = 16 which is our UnUn transformation ratio
As for the coax loop, sincerely I don't like it so much and I don't like the way it's connected to the coax, I'd probably use a tapped 1:1 transformer, say 5+5 turns with a tap at 3 turns on the secondary, the untapped winding would then go to the coax while the tapped one will be connected to the loop ends with the loop shield connected to the center tap, such a config would allow to mantain the loop balance; notice that you can do that with your NooElec balun, once you cut "R1" you just connect the coax loop braid to the center tap and you'll have exactly such a config
But again, just try the loop idea at my previous post, also since a random wire will probably be "too noisy" for your location