Right, I think we've actually circled around to our original thoughts about why he referred him to the SDNY.
If I remember, We assumed that he did so in order to let the state pick up any state charges. That was directly in relation to Drumpf being able to pardon federal charges preemptively. If the investigation takes place in NY, it makes sense that the SDNY handle that information. It also allows for Schneiderman and now Underwood to remain in close proximity to the investigation. Since the suspected crimes took place in NY, they would ultimately be the one's prosecuting in the case of state crimes being brought.
Now, the Feds would get first crack, but if the Feds charge, Drumpf will be tempted to pardon. So Mueller can basically say "If he pardons you preemptively, you'll be charged at the state level."
Either way, If Cohen doesn't spill the beans, he's spending the rest of his life in jail, and his family will be bankrupt. So, he only really has 1 viable option, and that's to flip.