Agent at the DL One kiosk at JFK T4 informed me after trying that she couldn’t through-check my bag to HNL and, as promised, I thanked her for trying and went on my way. Thanks again for the information.

[6/17 update]
My HNL-MSP-LGA trip went pear shaped this morning when MSP-LGA was cancelled and I got auto-rebooked HNL-SLC-DTW-LGA. I was able to find a MSP-JFK flight with a nine hour layover to preserve my DeltaOne leg and the nice agent at HNL didn't blink an eye when I asked her to through check my bag to JFK.

[7/6 update] I’m flying the same JFK-LAX-HNL itinerary as last month and this time, I was able to get an agent who was willing to through-check my bag to HNL.