This is very similar to how our currency eMunie works.
All new transactions are verified all the way back to the "genesis" block/transactions, via forward and backward lookups that will yield the same path if its valid. These results are signed by whats called a "hatcher" (it births transactions into blocks), this block is then passed to another randomly selected hatcher that checks it again.
After a n number of confirms specified by the sender, the transaction makes it into the chain.
New currency is "voted" in, and distributed around the system depending on who's done this task and how many times they have done it.
There is a thread on the boards that explains it more if you want to look how we propose it. Very similar to what you are suggesting but ours works on consensus and trust.
Sounds nice. But, where's the code?