I don't get why you want "efficient distribution of money" ? Are we talking distribution of wealth?
Any system you try be it CPU mining , centralized mining and then distribution by an "authority" or any other system you think of is doomed to fail. Wealth goes to wealth and that's that. Even if you annul all current wealth in the world and distribute equal amount of your new altcoin to each and every person on the earth within a very short period of time that coin and wealth will move to a top few percent once again.
If you read my prior two replies, I hope it is becoming clear that I view capital as knowledge. Money is just a claim on future human labor. But unlike menial labor, knowledge work is not fungible. Read the linked papers in my OP to understand why I believe this changes everything.
Money will now be almost entirely useless as a store-of-value and only as an exchange-of-value.
We will store our knowledge in the code.
We will use money only to exchange the value in our code.
The non-code economy will shrink relative to the code-economy.
Everything will change.
The Bitcoin ponzi is the last big bang of capital, as capital is running around like a chicken with head cutoff and can't find a safe haven. Because there is no more safe haven for capital. Capital is dying. A knowledge phoenix will follow.