Interesting and detailed article. Kudos.
The Federal Reserve has TWO mandates: keep a low target of inflation (approximately 2%) and to keep low unemployment.
Unfortunately these two mandates can sometimes conflict with one another. Notice that the mandate is not FULL employment and a gap has been created whereby 4% unemployment is considered "full" employment. Your comments on the 1970s with double digit inflation is a good example of the clash between the two mandates.
You are absolutely right- economics is not physics and they only thing the Federal Reserve decision makers have to go on is theory and here is where I consider the biggest gap. On what theory do you base your analysis and decision?
The Fed, when created, existed in a world of classic economics underpinned by gold standard (commodity based) currency and all their actions, including a terribly poor response to the Great Depression, was based on classic economics. Later economists in the Fed (and government) evolved to follow Keynesian economics which for a long time much better matched the real world and was far more useful than basing decisions on classic economics.
Some in the political-economic world revived classic economics with an element of Say's Law (supply side) - see Reaganomics but the reality is that this didn't result in the outcomes they predicted. However ultimately both Classic (the older version and the revised version) and Keynesianism were rooted in gold-standard approach to economy pre-dating the rise of the internet and true global trade networks.
Ultimately the theory approach needs to evolve. I firmly believe the better theory to answer our modern economic issues is Modern Monetary Theory (MMT)