If the puppeteer forced low-tax firms to finance with debt, and high-tax firms to finance with equity:

The IRS would collect no corporate income tax from the low-tax firm. Low-tax investors who do not mind interest receipts would preferentially sort themselves toward the low-tax firms. With a 4% tax on $100 interest receipts, the IRS would collect $4 from them.
The IRS would collect a full $40 from the high-tax firm. High-tax investors who like equity gains would preferentially hold their shares. The $60 paid out to investors would face a 10% capital gains tax rate, for another IRS take of $6. In sum, Uncle Sam ends up with $46.
The total tax payment would therefore be $4 + $40 + $6 = $50. This is much higher than the $15.80 tax in our proposed best solution. So the answer to our original question is yes—Uncle Sam would be better off if he could eliminate the tax deduction of interest for high-tax firms.