Noisy loop 1: Untuned active loop antenna
At first I tried using the wire as a receive-only, active loop antenna along the lines of M0AYF's untuned active loop antenna. I had previously had good experience with this active loop antenna, using a long, 3cm-wide copper strap formed into a square shape having approximately 0.75 meters per side. However, when I now tried the same loop amplifier with the larger 4m x 2m wire loop antenna, the noise was much higher than I expected.
Noisy loop 2: Tuned, passive loop antenna with large air-core transformer (auxiliary coupling loop)
Next I tried tuning the antenna with a small variable capacitor. To get the signal to the receiver, I used a random-length of 2mm-diameter wire, probably about 1 meter long, formed it into a loop, and clipped it to the main antenna element. The coaxial cable going to the receiver was then connected to the ends of the smaller auxiliary coupling loop. This is a common way to feed small transmitting loop antennas. Though this antenna does not qualify as "small", the principle is the same -- a loosely coupled auxiliary loop serves to transfer energy from and to the main resonant loop.
Compared with the untuned active loop antenna, I expected much quieter performance with the tuned loop. However, performance only marginally improved. The noise level was consistently high across the entire tuning range, though strong signals could be brought up out of the noise by peaking the signal with the variable capacitor. Overall performance was very poor.
I then noticed that simply connecting the auxiliary coupling loop to the receiver, even without the coupling loop near the main resonant loop, resulted in an increase in the noise level of the receiver. Therefore, the auxiliary coupling loop -- all by itself -- was picking up some kind of local noise, through electric or magnetic coupling. The noise is probably ambient electric-field and possibly magnetic-field noise produced by electrical appliances of other nearby residents.
A quiet loop: Tuned, passive loop antenna with small ferrite-core toroidal transformer
I wound the resonant loop's wire element twice through the ferrite core, and made a secondary winding of three turns, that then connected to the coaxial cable leading to the receiver. For mechanical convenience, the ferrite transformer was located next to the corner-mounted tuning capacitor; such a location for the transformer increases (compared to the typical transformer location diametrically opposite the capacitor) the impedance seen looking into the transformer. Considering both the higher-impedance location of the transformer, and the ad-hoc turns ratio on the transformer, it is certain that the resulting impedance transformation is incorrect (i.e. it does not match exactly to 50 ohms) and will need to be corrected when I adapt the antenna for transmitting. But for receiving, we can tolerate some degree of impedance mismatch.
The result of using the transformer, for receiving, was as hoped: a dramatic decrease in noise levels, along with high signal levels when the capacitor was peaked to the reception frequency. Though the loop balance is compromised by the asymmetrical construction (due to the corner-mounted capacitor, and the capacitor-sited transformer), the loop was nevertheless comparatively quite immune to the local noise, meaning that there was not significant noise ingress via common-mode current.
Therefore, in an environment with high levels of nearby electromagnetic noise, the ferrite transformer method for coupling to a loop antenna may be more immune against near-field noise than a larger, air-core transformer formed with the traditional auxiliary loop.
Analysis: Balance, common-mode currents, chokes
For the other two antenna configurations that were comparatively noisy -- the untuned active loop antenna configuration, or the passive tuned loop antenna with air-core auxiliary coupling loop -- if we assume the cause of the noise is imbalance in the loop, and that the imbalance is allowing the noise to induce common-mode currents, then it is possible that using a common-mode choke on the feedline might be able to reduce the noise to acceptable levels. Due to the geometry of the balcony, perfect symmetry in the loop construction is impossible, and even if it were possible to construct the loop with maximum physical symmetry, the environmental asymmetry will always unbalance the antenna to some extent.
Regarding the auxiliary coupling loop: perhaps one intuitive explanation would be to say that as the auxiliary loop becomes large (due to the main resonant loop also being large), then the auxiliary coupling loop itself starts to become more sensitive to balance, and any imbalance in the construction of or environment around the coupling loop itself will allow common-mode currents to flow. There may also be other mechanisms at play that could explain the noise ingress. There is a construction method that involves shielding the coupling loop; this technique may improve balance within the coupling loop and may reduce the common-mode currents and hence the noise ingress. An experiment, comparing the noise ingress in an isolated coupling loop and in an isolated and shielded coupling loop, could determine if shielding the coupling loop would help. But in this particular case, with this large 4m x 2m wire antenna, there seems to be no practical advantage of continuing to investigate the use of a comparatively large auxiliary coupling loop; a ferrite transformer is more convenient and seems to have no disadvantages.