What low output moving coil cartridge do you own or want to own to use in your system? Perhaps the easiest approach would be to make that information known and then just get advice on what step-up ratio will work best for that cartridge. It is helpful/necessary also to know the internal resistance (= output impedance) of the cartridge itself.
What Al is telling you is that the ratio of the signal voltage seen at the input to the phono stage to the signal voltage emitted by the cartridge will be equal to the turns ratio of the SUT. However, the ratio of the output impedance of the cartridge (= its internal resistance) to that of the input impedance "seen" by the cartridge will be equal to the SQUARE of the turns ratio. (I realize you've got most of this already; sorry to sound pedantic.) So, say your MC has an output of 0.5mv and an internal resistance of 10 ohms. Say your SUT has a 1:10 turns ratio and that your MM phono stage presents a 47K ohm impedance. The phono stage will receive ~5mV of signal voltage (10 times 0.5), if the impedance matching permits, and the phono cartridge will see an input impedance of 470 ohms (47K divided by 100 or 10-squared). That is a typical OK match-up. You want the input impedance to be a multiple of the cartridge impedance. Classically, a 10:1 of impedances is ideal, but it is not a problem to go down to 5:1 and even lower. However, in this case we have 10 ohms looking at 470 ohms. We are way into the safety zone with a ratio of 47:1. What Al and one of your references was saying is that if the input impedance gets down close to the same value as the output impedance of the cartridge, then the total 5mV of signal is no longer deliverable to the phono input stage; some of it goes to ground and is wasted.
To add to the mix, some might decide that the cartridge sounds a little tizzy with this 47:1 ratio of input to output impedance, so to dampen the high end response of the cartridge they find ways to reduce the impedance ratio, such as to introduce a resistor that is seen by the SUT to be in parallel with the 47K ohms afforded by the naked phono stage input. In the end, you might decide that this cartridge sounds best when it sees a 100 ohm load. In that case, you could add a resistor in the range of 11K or 12K ohms, in parallel with the 47K to produce a net resistance of 10K ohms on the secondary side of the SUT. Now the cartridge will "see" 100 ohms across the SUT/ (10K divided by the square of the turns ratio).
What Al is telling you is that the ratio of the signal voltage seen at the input to the phono stage to the signal voltage emitted by the cartridge will be equal to the turns ratio of the SUT. However, the ratio of the output impedance of the cartridge (= its internal resistance) to that of the input impedance "seen" by the cartridge will be equal to the SQUARE of the turns ratio. (I realize you've got most of this already; sorry to sound pedantic.) So, say your MC has an output of 0.5mv and an internal resistance of 10 ohms. Say your SUT has a 1:10 turns ratio and that your MM phono stage presents a 47K ohm impedance. The phono stage will receive ~5mV of signal voltage (10 times 0.5), if the impedance matching permits, and the phono cartridge will see an input impedance of 470 ohms (47K divided by 100 or 10-squared). That is a typical OK match-up. You want the input impedance to be a multiple of the cartridge impedance. Classically, a 10:1 of impedances is ideal, but it is not a problem to go down to 5:1 and even lower. However, in this case we have 10 ohms looking at 470 ohms. We are way into the safety zone with a ratio of 47:1. What Al and one of your references was saying is that if the input impedance gets down close to the same value as the output impedance of the cartridge, then the total 5mV of signal is no longer deliverable to the phono input stage; some of it goes to ground and is wasted.
To add to the mix, some might decide that the cartridge sounds a little tizzy with this 47:1 ratio of input to output impedance, so to dampen the high end response of the cartridge they find ways to reduce the impedance ratio, such as to introduce a resistor that is seen by the SUT to be in parallel with the 47K ohms afforded by the naked phono stage input. In the end, you might decide that this cartridge sounds best when it sees a 100 ohm load. In that case, you could add a resistor in the range of 11K or 12K ohms, in parallel with the 47K to produce a net resistance of 10K ohms on the secondary side of the SUT. Now the cartridge will "see" 100 ohms across the SUT/ (10K divided by the square of the turns ratio).