Loop antennas and long wire antennas work completely differently, and even a smaller loop on the Wellbrook amp should pull in AM signals perfectly well. However, if you are trying to use the loop indoors it may be in a dead spot where the signals are completely overwhelmed by noise from within the house – you really need to try it outdoors or in an upstairs window to give it a chance. A few feet from your computer is not a good place for evaluation!
As for thin wire loops, they will also work, but not as well as something fatter, which is why most amplified loops use something like 20mm copper or alu tube instead. Coax cable when used in a loop simply becomes a tube of the same diameter as the braid, so it’s better than a plain wire but not as good as the 20mm tube. It’s all to do with getting the lowest possible inductance to get the biggest currents flowing around the loop, and the bigger the surface area of the conductor, the smaller the inductance – hence fat tubes are better than thin wires.