If you're willing to chance it for the most part you'll be able to find a US gateway - HND/NRT - SIN on NH J close in for ~100k miles. I currently have EWR-SFO-SIN booked for 180k on UA for 2 weeks from now because my dates are inflexible or I would have waited to book so this is my backup option. I'm seeing some NH options pop up so hopefully the trend continues.
Pre-COVID NH J/F availability used to be pretty good close in. I've been following availability for a few weeks now and it's definitely less than it used to be but I'm not sure if that is just due to loads or just because of the holidays.