I don't have the answer to your income inequality concern, but I've been reading about it a lot lately. Came across this relatively long article on it yesterday, which from my recollection seemed to mainly point the finger to breaking up the labor unions, but I certainly found it interesting if you have 20 minutes. It argues almost nothing you can do via taxes can solve the inequality issue, although it admits the new bill won't help.
Why Stopping Tax “Reform” Won’t Stop Inequality
https://www.nakedcapitalism.com/2017/12/stopping-tax-reform-wont-stop-inequality.html
I think I found one a few weeks ago which I linked mainly pointed to the unavoidable consequence of globalization, and pointed out that while "inequality" has risen, worldwide poverty has decreased sharply. So is inequality rising, or are dumb american white people just losing their market share?
We don't disagree on the rest of what you say. We probably just need to agree people should work until they're 70 and push back SS and medicare till then. Most people are already working till they're 70 unless they're a govt employee. Then just tie the age to life expectancy (which is now gone down 2 years running).
The best compromise would involve doing the above with also a testosterone admission that we can probably get by being weaker militarily. People aren't going to beat us with better stealth bombers, they'll beat us with hacking our electrical grid or sneaking some anthrax into NYC.