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Here's the basic idea of what I'd think is fair
You have a basic rate for income below the 20th percentile of all incomes
Multiply that by 1.5 for income between that and the 40th percentile
Multiply that by 1.25 for income between that and the 60th percentile
Multiply that by 1.125 for income between that and the 80th percentile
Multiply that by 1.0625 for income between that and the 95th percentile
Multiply that by 1.03125 for income between that and the 99th percentile
Multiply that by 1.015625 for all income above the 99th percentile, with the additional caveat that people who top this bracket even once cannot hold public office, donate to political campaigns, or hire lobbyists and lobbying firms for ten years following them topping out.
Imagine something similar for taxes on units of housing owned, dividends earned, and so on and so forth.
The idea being that the highest rate can't be adjusted without significantly reducing the tax burden of the poorest, basically erasing the only way conservatives have been able to balance the books whenever they try that shit.
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Not more complicated than current US income tax system. Maybe a few more tax brackets...
I think I also made it a bit more flexible to, by only making one number changeable and fixing the brackets to percentiles, the system functions more or less independently year to year, with the single dial being all that can be turned when revenue needs to be raised from across society or when a break can be handed out due to a miraculous surplus or occasion for national reward.
Specific example: I think you may want to check your rates, the rate differential between highest and lowest in your example seems much lower than the current system. General idea: Couldn't the rates just be adjusted to the base or unlinked later? Changes would have to be legislative anyway.
I kinda pulled the exact multipliers out of my butt, however! I've spreadsheeted this shit out and there's a way to do it such that 60% of Americans wind up with a tax break while putting some serious screws to obscene wealth in the highest brackets. I even added an additional multiplier for every multiple of twenty times the average of the lowest quintile's wages someone's income rises above. Twenty because that's the predicted "ideal" wage ratio between an organization's lowest and highest compensated members.
So you have the top bracket rate, and then after the first multiple is passed, that gets taxed at the nominal rate times the multiplier, and so on and so forth past each new multiple.
I really think you should re-address your idea on a theoretical framework. It's difficult to imagine that a new set of income tax rates would address extreme wealth or address the crises of capitalism regardless of the numbers you have in your spreadsheet. For example, OP suggests using total wealth as a tax base to alleviate inequality which would be a new way of approaching the issue.
If you'd still like to use income tax rates to approach inequality, I would suggest starting with high negative percentages and increasing them through your table. Kinda like this:
base * { -99%, -98%, ....., 99%}Sorry if this comes off as harsh, I appreciate that you're looking to for a way to address these issues.
My brother's making an app to do something like this!! Check out the video and let me know what you think... https://www.indiegogo.com/projects/comingle#/