For a resistive load, an increase in plate voltage will decrease current through the tube, reducing the cathode voltage which causes the current to rise and the plate voltage to stabilize. in other words the resistive load has a feedback loop which stabilizes the plate voltage by changing current.
This little nugget explains some other choices Bottlehead made. To resist that change in cathode voltage, convention has suggested a large capacitor across the cathode resistor to stabilize its voltage, but this capacitor sees signal current, so instead carefully chosen LED's were used instead that maintain nearly a constant voltage over a wide range of current draw.
Yes! i was quite pleased with myself when i was looking over the Crack schematic and noticed how the LEDs would be beneficial.
The last piece of the puzzle has to do with load lines, I suspect that is buried in the links provided.
I haven't spent too much time with tube load lines but ill give it a shot. The CCS line should be flat, or close to it. Would the advantage here be that the resistive, negatively sloped, load line crosses over the less linear portions of the current vs voltage graph? i believe that relates to distortion.