• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
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Single output OPT for 4-8 ohms speakers

A higher impedance load also needs higher primary inductance.
When connecting an 8 ohm speaker to a 4 ohm tap, there will be LF loss as the output transformer has not enough inductance for a "real" 6k primary.
You would need some 50H of primary inductance; the 3k transformer would normally have no more than some 25H when it is wound correctly.

I think this is what the guy I vaguely remember meant.

So the 6k:8 or 4.5k:6 would be preferable than 3k:4 then?
 
Generally, for a 300B single ended amp that does not use negative feedback:

Lower primary impedance will give:
More power; More distortion
Lower damping factor;
Lower plate voltage gain, But Lower voltage reduction from plate to output tap
(those last two factors tend to partially cancel).

Higher primary impedance will give:
Less power; Lower distortion
Higher damping factor
Higher plate voltage gain, But Higher voltage reduction from plate to output tap
(those last two factors tend to partially cancel).

Compare two manufacturers single ended output transformers that both have a primary impedance rated at 3k:
One may have 15H primary inductance, and the other may have 30H primary inductance.
One may be rated for 100mA DC, the other may be rated at 50mA DC, respectively.
If you operate the 300B at 300V plate to filament, and -61V bias, that gives 60mA plate current.
In that case the 100mA transformer with only 15H is probably going to give a better low frequency output (less saturation and less distorted).

Another generalization:
A transformer that has one primary impedance and only one secondary impedance might be optimized for the best frequency response and best square wave response (when loaded with the proper load resistor).
But when you put a loudspeaker on it, that might no longer be true, because of all the different impedances and phase angles versus frequencies.
And there is the issue of two different model loudspeakers of different nominal impedance ratings.

A transformer that has one primary impedance and two secondary impedances might not be optimized for the best frequency response and best square wave response (when loaded with the proper Load resistor).
Putting a loudspeaker on it is not the same as the load resistor, the loudspeaker impedance and phase angles will be different at different frequencies.

But when you put two different model loudspeakers on, and use the best output impedance tap for the particular model loudspeaker, it might give a better result than the single output tap transformer.

There is no one sure answer here. Too many variables.

If you want to use Edcor output transformers, it might be good to check with them to see if they will wind a 2 output impedance taps for a little more money.
Or look at various output transformers that have multi tap outputs.

Again, at least measure the DCR of your different loudspeaker models.
Also, consider the different rated efficiency of the different models.
Caution:
Some efficiency dB at 1 Meter ratings are for 2.828Vrms, and some others are for 1 Watt.
2.828Vrms into 8 Ohms is 1 Watt.
2.828Vrms into 6 Ohms is 1.33 Watts
2.828Vrms into 4 Ohms is 2 Watts.
 
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I think 6A3sUMMER said it well: "There is no one sure answer here."

I'll just a a note that the treble is also an issue - operating at a higher impedance than designed will reduce the impact of leakage inductance and increase the impact of winding capacitance.