Mainstream economists know that CPI isn't accurate because of changes in demand. So they created other indicators (like chained CPI [0]) to account for changes in the basket of goods.
Normalizing against the M1 is an not very meaningful because ignores the fact that the price of a dollar is subject to demand as well. In times of high demand for dollars (like right now), the supply of money (the M1) needs to increase to for the price of a dollar to not rise.
In other words, stock prices normalized to the M1 has the same amount of meaning as stock prices normalized to the number of loaves of bread the country produces, or the number of cars. It's nonsense — you're comparing a price to a metric that only takes into account half of the equation (only supply)!
Sidenote: When the price of a dollar rises, that's deflation; when it falls, that's inflation. That's also why "asset price inflation" isn't precise — inflation measures the change in price of a currency, not an asset. Maybe individual assets go up or down in price, but that happens in response to consumer demand shift. The Fed's mandate is to manage inflation, which is affected by changes in aggregate consumer demand. Therefore, Congress delegated it tools to influence consumer demand as a whole, but not tools to shift demand from one asset to another.
The phenomenon you're observing is: the Fed's monetary policy helps the US grow, which benefits corporations and increases stock prices. The only way the Fed can prevent that is to... stop the economy from growing by letting our currency deflate? Which sounds bad? I.e. the Fed can't do anything to shift consumer demand, short of causing a recession.
TD;DR: If you think stonks are overvalued, then blame Congress, not the Fed. They're the ones who have the power to change that without causing a recession.
[0] https://www.brookings.edu/blog/up-front/2017/12/07/the-hutch...