Its not Miner A vs. the Pool and Miner B vs. the pool
Its Miner A vs. Miner B.
The distribution doesn't matter very much, because miner A and miner B both receive it the same system. I arbitrarily picked the averages out of the thin air. I can do that, because on the pool at any given time we can find miners all over the scale. That's why I can say miner A has this distribution, because no matter what, I can find a miner with that average.
To put it another way, its pointless to argue over weather miner A with average X would really distribute that way. Even if you are right, there is another miner with average Y who WOULD, and I can pick any of them since the competition is between the two miners, not miner vs. pool.
If the distribution is not that of a Poisson process, all your results will be wrong. Otherwise you are not simulating a Poisson process (which hashing is). If you like, I can change the script I wrote to a per block reward system, I'm sure it would come out the same. If not, I concede.
Which reward scheme is middlecoin using anyway? I have no idea. But I don't think it's per block reward.