>The JD staking wallet does often have two outputs which are able to stake at the same time, and so only the first of them gets to stake.

It may be so, but I was more curious about the the actual hashing events being serialized.  Lets say a a wallet had 1 million inputs, then how long would it take hash all 1 million inputs? My guess is the first 1/2 million would have a greater probability to stake and not orphaned then then last 1/2 million just due to the time it takes to do hashing. 

Doesn't the 1st person who has a valid stake and propagates over the network win?