[Reserved for clarifications/questions/etc.]
Based on feedback from mhps on the Peercointalk forum, who pointed out the potential for blockchain bloat due to having substantial numbers of PoC transactions in each block, I have added this:
Let the expected-time-to-check-in (ETTCI) scale with the number of non-PoC transactions included in the last 24h of blocks. Create the algorithm such that the target is no more than half of the transactions in a given block are PoC transactions. If the coin is lightly transacted and there are lots of stakeholders, then maybe the ETTCI might scale to 7 days or even longer. But as non-PoC transactions get more numerous, the ETTCI will become faster.
Refinement of the original idea by removing PoC transactions from the blockchain and consolidating them into the coinbase transaction, which will pay out PoS earnings to all who sent valid PoC transactions:
Each block mined will distribute PoS earnings to ALL addresses who sent PoC transactions which would have been included in that block. So the PoC transactions aren't added to the block explicitly, but the addresses will receive outputs from the coinbase transaction which will be the payout of PoS earnings, based on the Stake-Days held by each address. The Stake-Days of those addresses are also reset to 0, since their Stake has been paid out. The actual miner of the block will also receive earned PoS + all transaction fees from that block, and their Stake-Days will also be reset to 0.
In this way, you earn your stake earnings by staying connected, even if you never have enough stake accumulated to actually mine a block. This also consolidates the PoC transactions into a single summary Coinbase transaction, which will hopefully cut them down in size. This ensures that everybody receives their stake payouts on a consistent and frequent basis.
Explanation of rationale, based on reply to ppcman on Peercointalk forum:
Firstly, an unstated assumption to my proposal is that I think this would have to take place with a pure PoS coin, i.e. not Peercoin but maybe a derivative. Given this, I want to get away from the word "minting" for pure PoS coins. It implies that there is a fundamental difference between PoW mining and PoS minting. There really isn't, although I can see how in a hybrid PoW/PoS coin like Peercoin, you would want to make the distinction, and "minting" is fairly clever.
The goal of Proof-of-Stake is to replace Proof-of-Work as a system to create and secure the blockchain. What is the goal of mining in PoW coins? Part of it is distribution of new coins (especially when a coin is first launched), but the major part is securing the blockchain. Similarly, the goal of PoS should not be to earn "interest" on holdings, but to create a secure blockchain without using ridiculous amounts of electricity. The PoS rewards should be enough to incentivize mining/minting. Given this, I actually think that the PoS earning rate in most coins is too low. For one thing, I think that all transaction fees in the mined block should go to the miner, regardless of their initial stake value. Yes, this would allow a PoS block miner to earn more coinage than he had to start with, if he had a small amount of coins to begin with and included a lot of transactions into his block. This is just the same as if someone were solo-mining in Bitcoin and found a block and received 25 BTC as his reward.
My proposal is trying to fix the problem of not enough people running active nodes, and not enough incentive to PoS mine. I don't care about the people that want to keep their coins locked away in cold storage. The more copies of the blockchain that are out there, and the more nodes that are propagating transactions, the better for the health of the network.
I think that the idea of people being able to store up large amounts of stake is flawed, and is part of what my proposal solves. People need to be transacting with their coins, and if they're not transacting with their coins, then they at LEAST need to be helping to secure the network. The only way for a coin to really be valuable is for it to be useful. And if they are incentivized not to spend their coins for 30-90 days, IMO that is a perverse incentive. I'm not saying that we need to punish people for holding their coins like the demurrage folks, but people should NOT be rewarded for simply owning coins, holding onto them, and connecting to the network sporadically and infrequently. That is pretty much like charity to the lazy. People should be rewarded for doing things that help the network, and rewards should be withheld when they do things that do not help the network. Keeping their coins in cold storage and never connecting to the network is not beneficial to the network.