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.
I believe OP idea of efficient distribution of money equates to a proper distribution of wealth as well as a good velocity of money being exchanged. It requires widespread usage.
As for bitcoin achieving good distribution of wealth as well as a good medium of exchange, we can already see how it is not going to achieve both