1. Measuring total compensation is just common sense. The data is right there. Not sure what your complaint even is here. You claim this is ridiculous — do you disagree with the data? On what basis?
2. By “correctly”, I mean by using consistent deflators, for example. Using different deflators would fail an intermediate econ exam. Again, the data measured correctly shows this differently. I am also referring to using net outpout as opposed to gross output — again, there is no debate here. It makes no sense to use a gross figure. It’s just misleading.
3. Increasing inequality is an issue (I agree here), but you CANNOT measure productivity of a whole against a subset of “blue collar workers”. This is basic statistics. If you’re examining the productivity-compensation link, you have to be consistent. Measure a subset against a subset, or a whole against a whole. You don’t get to pick and choose.

I would also encourage you to check out Stansbury-Summers (2017):

Productivity and Pay: Is the link broken?

It found the link for median workers still largely intact.