If you buy a $100 widget today, you pay $77 for the widget and $23 in hidden fed tax costs- but you don't see it on the receipt.
This just isn't true. The 22% "embedded federal tax" is a myth. You are misrepresenting the study you are quoting (besides that study being flawed).
Twenty-two percent of everything sold in the U.S. plus exports would mean the "hidden fed tax costs" would be $2.31 trillion! The total taxes paid by businesses in 2003 was $488.25 billion, and most of that was payroll taxes which virtually every economist agrees is really paid by labor through lower wages. That leaves a minimum of $1.8 trillion for business tax compliance costs! Most reasonable economists put the number around $100 billion. Let's double that to $200 billion to be fair, that leaves $1.6 trillion.
The numbers don't add up.
The vast majority of economists believe that the incidence of corporate taxes are born by investors in the form of lower returns and labor in the form of lower wages, not consumers paying higher prices.