I like the idea of probabilistic PoS. I think the motivating problem is exaggerated but this could have other advantages too.
Another way (not sure if easier are harder to calculate) is to have the mod of the previous block hash deterministically pinpoint a single satoshi from a coinbase transaction. Then follow that satoshi as it travels from transaction to transaction until it reaches an unspent output. Then that output address will be selected as the next stakeholder. You can do this deterministically. Since the initial satoshi picked from a coinbase output is evenly distributed, the eventual selection will be evenly distributed also. I can explain more if people are interested in how this will work.
I don't think satoshis are tracked the way you think they do. If there's a 50 BTC coinbase which is split to two addresses you can't say "this satoshi went to output A and this satoshi went to output B". Not a major problem though, if you agree on a randomness seed (deterministically from the blockchain) you can simply trace the chain forward, in each step choosing a random output weighted by number of coins.
Satoshis are not tracked that way, but you could track it that way. You just need a deterministic way to do it. So just map every satoshi in the input to a satoshi in the output using an ordered 1 to 1 mapping. So for example, if you are looking at a transaction with an input of 50 BTC and 2 outputs of 25 BTC each and you are tracking the a satoshi that is located at 26.11111111 of 50 BTC, then you would follow the 1.11111111 satoshi in the 2nd output. Does that make sense?
Yes, you could do that. You need to be very careful though not only with the order of inputs and outputs, but also with the order of transactions in a block since the satoshi can end up as a tx fee.
Essentially this is equivalent to how I suggested to look at it.
There is a standard ordering of transactions in blocks, right? If not, having it alphabetized by address is fine. As long as all the nodes use the same deterministic way, we are good. Satoshi ending up as a fee is fully supported. Since those will just be sent to the miner's block reward and it can continue follow the path.
The only catch is it's possible for a miner to destroy coins by not redeeming the full 50 btc in the coinbase. When that happens to our tracked satoshi, maybe we decide that there's no stakeholder for the next block.