Thank you both, Frank and Bob. After contemplation, some rambling follows:
I'm still not quite sure what the best "real" primary impedance is, but from some research and from what Steve Deckert wrote here (
https://www.decware.com/cgi-bin/yabb22/YaBB.pl?num=1464381300/3), it sounds like in your case Frank the real primary impedance would be more like 5.3 kOhms when using the GXSE10-6-8K with 4 Ohm speakers.
In the same way, Bob, it makes sense that 6 Ohm speakers plugged into the 4 Ohm tap of a 6.6 kOhm transformer would really be more like 9.8 kOhm to the tube.
Steve actually makes it sound like the best solution for 8 Ohm speakers would be to use transformers with an even higher primary impedance than 10 kOhm and secondary impedance higher than 8 Ohm to pull the real primary impedance back down again (e.g. fictional example 12k primary to 12 Ohm secondary would only be 8 kOhm when connecting 8 Ohm speakers. At least that's the way I understood it.
Since I am lacking actual knowledge and can't just try different output transformers, I will probably just try finding one in the Edcor GXSE series that's wound for 8 Ohms secondary with a primary in the 5k-9k range… still not quite sure what difference this makes in terms of sound. :o