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.

How can we improve upon Bitcoin's highly concentrated coin distribution?

Only the top 3% should be power-law concentrated, the rest distributed with diffuse gas random concentrations:

"Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States" by A. A. Dragulescu and V. M. Yakovenko

We shouldn't give coins away to the lazy who do nothing to earn them, because Risto explained that in Russia the recipients just squandered the gifts.

Ideas thus far:

1. Decentralized CPU-only proof-of-work, but the threat are botnets

2. Centralized premine then distributed with a faucet first-come, first-served until depleted.

3. Centralized premine then distributed to merchants every month or quarter evaluated to be bonafide. So this really requires hiring staff, which should be paid either from premine or a foundation with membership fees.

Hit me with ideas please!

I will keep self-moderation to an absolute minimum but please try to stay on topic and no ego battles.