I'm wondering if Alaska may pull out the "they are booked in two different PNR" cards and say no to any compensation. Some airlines aren't even allowing agents to add in other airline segments or connections - everything has to be booked at the same time from the same source!
There also could be an issue in JFK because of the overnight "storage" of bags. TSA sometimes won't allow it depending on the circumstances - and being a large international airport, it very well could be a local TSA rule...
let us know how this turns out!