Now, I think that the source of our disagreement are diverging intuitions about free will and IQ.

I think that I can boost my IQ to some extent by exerting willpower; the amount of "thought power" in relaxed, normal and extreme-effort states seem to differ quite substantially.

You may see IQ score as the measure of maximal "thought power" (like when one passes IQ test when fully rested with no distractions and making his best effort); it makes IQ more or less constant, but a worse predictor of success, since success is more determined by average cleverness rather than peak cleverness.