First, this is not PPS. The math used resembles what is used for calculating the PPS reward but it's used for a very different purpose.

You're trying to think about this in terms of how it's done in a pool. This method does not have the concept of a round, therefore it's hopping proof. There is nothing to hop into or out of in the first place. A buffer is also nonsensical since there is no trusted party aside from Bitcoin itself.

When you mine in a regular pool, the pool keeps track of the shares you submit and calculates a payment to you accordingly. With the method I'm suggesting, You get paid whenever someone who is mining for your address, finds a block.

The trick is that the coinbase transacion can pay any number of addresses in a single block. That is how p2pool handles the payments.

I'll try to make this clearer with a simplified example. Let's assume you were mining fast enough to find a block per month on average. You also have 29 friends who are also mining at the same speed. If all of you mine separately, each of you will find 50 BTC per month on average but sometimes several months will go by without you finding any.

Because you'd prefer more steady income, you get together with all 29 of your friends and agree that whenever one of you finds a block, everyone will get 1/30th of the block reward. Assuming everyone does this, each of you will then receive 1.67 BTC on average every day. However, the problem with this setup is that it's very easy to keep mining to yourself and take the 1.67 from everyone else and no-one can prove that you're doing that.

We need a way to make sure that everyone who is participating is actually mining according to the agreement, otherwise it just falls apart. The way this has been solved thus far is by pools. Everyone mines to the pool's wallet(1) and the pool receives shares from them proving they're doing so. It's then the pool's job to calculate how much of the payment belongs to each participant and pay them accordingly.

The way I'm proposing is another way of solving this, without any kind of trusted intermediary(2). In my system, you and your friends would each keep mining separately. However, each time you find a block that meets the share difficulty, you send that plus the coinbase transaction to each of your friends. Your friends will do the same. Based on the shares your friends have sent you, you can check that they're sticking to the agreement and actually mining for you too. The end result is that each time you or your friends finds a block, all of you will be paid the agreed on amount.

However, in practise it's quite rare that everyone mines at the same speed. That's where the Tit for Tat algorithm comes in. The Tit for Tat algorithm means that if one of your friends stops mining or just slows down, your miner will mine for them at the previous allocation until the value of the work you've done for them hits a predefined limit. After that, it will redistribute the block reward allocation to match the new hashing speeds.

I hope this clarified the misundestanding.

(1) Eligius and p2pool are exceptions to this as they actually pay directly from generation to the miners.
(2) Even p2pool has a kind of trusted intermediary. It's called the sharechain.