I did indeed focus on the first two clauses in your list of things 'the Fed cannot accomplish'.
The Fed indeed has little control or influence over the distribution of income (or wealth) in the country. Nor can they directly affect 'the burden of home ownership'. [But their easy money policies of 2001-2006 made it possible for any Tom, Dick, or Harry to get a home loan, as the country was awash in 'funny money'.]
But I am having a tough time seeing how your proposed tax changes would reduce inflation. If we are going to increase taxes on the wealthy, and reduce them on the lower income brackets, that would imply more spending by the less wealthy...which would be inflationary, in and of itself. [Unless you really believe that all the less wealthy people would take their tax cuts and use them to reduce their debt levels, instead of spending them on new consumer goodies; and if you believe that, I got me some good dry swampy Florida real estate to sell you---real cheap!!]
Combine your tax changes with a tight money policy, and we might be able to get this country on the right path again...