Let me reword then: Current stays constant, and voltage goes up as the load impedance goes up. This is the opposite of voltage-source (or "constant voltage") amplifier behavior, which we see in solid state amps.
Maybe I'm missing something?
Let me reword too

You are conflating "maximum power output vs load impedance but independent of input voltage" with "power output vs load impedance given a constant input voltage (and while in a linear operating region)".
To put it another way, "constant current" and "current limited" are not the same thing. You can have a current-limited voltage source.
For argument's sake, suppose you have a current source that delivers 5A out for 1 V input. Into 4 ohms, you get 100 W. Double the load impedance to 8 ohms, current stays the same, you get 200 W. (Provided the voltage limit is not reached). That is what you are thinking of.
Now suppose you have a voltage source that produces 20V from 1 V input. Into a 4 ohm load, you have 100W. Into an 8 ohm load, the current halves, and you have 50 W output. Hopefully we agree so far

Now suppose that this voltage source was limited to producing 5 A output. And let's say it's maximum output voltage (provided current limit is not reached) was 100V. So with 1 V input, with the 4 ohm load, we are at maximum power output - 100W. When we double the load impedance to 8 ohms, however, we have halved the current output. So we are
no longer at maximum output. We also have to double the input voltage to 2V to get back to maximum output. So, with 2V input, we have 5A and 40V on the output. 200W.
So, with a
current limited voltage source, the
maximum power output increases as impedance increases. (Up to a point, of course, until the voltage limit is reached.) That does not make it a current source.
Now, I don't know the specifics of Roger's amp but I have run into this with another OTL. (Which I only half built due to the issue of power output suddenly become much less than expected when the real current capability of the output tubes I bought was discovered.) I was simply trying to point out that equating the increasing
maximum power output with high impedance or current-source behavior is not correct. FWIW Roger did say in the OP "When the amplifier clips it runs out of current rather than conventional tube or transistor amps which typically run out of voltage." and "This is because in mono the current doubles and thus the power quadruples."

J