What are the two different adjustments being uses? You're making some bold hand-wavey claims without showing your work.

"Because we are looking at a ratio of nominal values, we don't need to adjust for inflation: the influence of the price level naturally cancels."

Again you're missing distribution! There's a reason they use a standard basket of goods. You're also completely ignoring imports and exports.

"Because we are looking at a ratio of nominal values, we don't need to adjust for inflation: the influence of the price level naturally cancels."

"For that ratio to stay so constant, productivity growth and wage increases must have approximately kept pace with each other."

Only on the aggregate. You can very easily find that executive and other high earner pay has consistently increased at a higher rate than the median workers. So if that ratio remained the same and the increases mostly went to the upper class, then there is less for the middle and lower class.