Earlier quoted context omitted.
How about a progressive consumption tax replacing the income tax to encourage savings? It might be impossible to implement... for now.
Replacing income tax with a consumption tax would see the super rich pay even less tax as they spend a smaller percentage of their income compared to those with a lower income. [edited to fixed a typo: "the" => "they"]
So, the super rich would indeed pay a smaller percentage of their income, only if they spend the same as an ordinary consumer, but they would pay much more tax (e.g. 60% after 1 million) if they spend everything they earn.
This would encourage them not to swap pieces of paper for real goods. It would make them have more money in the bank but less million dollar cars and yachts. The productivity saved from not producing those non-producing consumer goods can be used, e.g., on farming, so that food becomes cheaper for the general populace.