I agree with your second link (by VK1OD).

The time varying magnetic field generates an electric field and that is
received by the loop. When you screen it completely, it doesn't work,
you need the gap.

By placing the gap opposite to the feed point, you get a balanced loop
without the need of ferrite or other constructions. If you can get balance
via other means, you don't need the screen. Balancing the loop reduces
noise due to common mode issues. This isn't different from using a balun
between a coaxial cable and a symmetrical dipole.

Your option three may behave competently different, as the coaxial cable,
power supply cable, switch mode power supply, etc may contribute to
reception of signal and noise due to common mode to differential mode
conversion.

From my experience (reception) with electrically small well-balanced
indoor loops and indoor dipoles, I found some advantage of the loop over
the electric dipole at low frequencies (say below 3 MHz). I contribute
this mainly because of the nulling capability. Whether is applies to your
location depends on the field distribution of the noise at your location.

At higher frequencies there is difference in S/N ratio, but not in favor
of one antenna. Sharp nulling wasn't possible. So to know what option is
best for you, you need to try it. Maybe install both options and select
the antenna that gives best results as this will depend on frequency and
the angle of arrival of the radiation you want to receive.

Other thing that may really help is to find your local source(s) of noise,
use lots of ferrites and try to find a sweet spot for best S/N ratio.

--
Wim
PA3DJS
www.tetech.nl
Please remove abc first in case of PM

So you are saying that cases 1 & 2 above are essentially equvalent if the
loops are balanced. In terms of noise rejection, there is no analogy to be
drawn between a shielded loop and a shielded cable.