For what's it worth I actually did end up booking my ticket today.
$2020 RT JFK/NRT
It was pretty painful.
Had to use a deep discounter to get that
If I only I had acted earlier, I could have done an AA CS from LGA to ORD, and then JAL from ORD to NRT (same routing on the way back) for only $1661
There was one upside, I'm booked in class W on the way back, so 100% miles for me.