I am very pleased to see such sophisticated statistical analysis. However, I have to oppose to some of your interpretations:

You cannot seriously say that "more government debt harms GDP". Considering Minsky's equation, Profits = Investment + Govt.Def., one can instead deduce that the causality is the other way around. When investment is going down, visible in a lower change in private debt, profits decrease. This has to be (and is, by some automatic mechanisms like taxes and transfer payments) offset by a government deficit or else you will get into a downward spiral towards a recession. So it is clear that the government deficit rises in times when GDP growth is weak.

I see the reason for the general trend of falling debt efficiency simply in the increasing financial sector. After all, the financial sector is essentially a zero-sum game, diminishing the proportion of credit going into the real economy, where it could generate surplus value. The historically low total debt efficiency we have right now is very plausible, considering that the FED's 'easy money' program boosts the financial sector only, neglecting the real economy.