You could minimize the accounting by setting a rebate level, then issuing a check to everyone (yes, even the rich people) for that amount.
To use your numbers, if you issued a rebate check for $100/month to everyone, the poor person would pay an effective rate of zero, while the rich person would still pay an effective rate of $400/month.
That just means you're moving the problem up a bit. The poor pay nothing, the rich pay relatively nothing and the middle class carries the highest burden.
You could minimize the accounting by setting a rebate level, then issuing a check to everyone (yes, even the rich people) for that amount.
To use your numbers, if you issued a rebate check for $100/month to everyone, the poor person would pay an effective rate of zero, while the rich person would still pay an effective rate of $400/month.