> the distortion curves .... it is either the second harmonic that rises with increase in output impedance
2nd harmonic cancels in Push-Pull.
> why the recommend load for 6V6 types jumps up at 250V (10K load) on the data sheets.
For marketing and historical reasons.
The 6V6 replaced the 6F6 and some earlier tubes.
B+ in home radios is traditionally 250V. (450V peak AC off the PT so 450V electrolytics don't blow at turn-on, 50V lost in rectifier, 150V lost in speaker field coil.) The two-6V6 radio is a big step up from the one-6V6 radio. In power and in cleanliness. The two-6V6 model does not have to be WAY better. In particular it is nice to have a plan which draws little more current than the one 6V6 (80mA vs 50mA, but a radio also has another 10mA-20mA in tuner tubes so 100mA vs 70mA), and/or can use the same iron as a two-6F6 model.
In a more liberal design, you raise the B+ and lower the load impedance to get a higher Output number for the specs.
And 8K or 10K are the same for any practical purpose (other than verifying that Ken-Rad got the test numbers right).
Optimum load for screen-limited push-pull tubes *does* go up as voltage goes down. But slowly. Peak current rises faster than G2 voltage, and vice-versa. Half the G2 voltage allows 0.35 of the peak current. Optimum load runs about inverse of square-root of voltage.
> For other output tubes .. recommend load drops or remains close to the higher voltage value when plate voltage is lowered
Tube amp design is about many factors. Sometimes a tube offers more current than we need. Then we may make the load the same or maybe lower when working at lower B+.