Who told you that NH and DL interline luggage? Just curious, it isn't clear in the post.
Generally DL will not do this (See link below), but in your case you need NH to do this. I don't know their policy.
https://pro.delta.com/content/agency...e-policy-.html
Having flown domestically in Japan, the process is different than internationally. The ticket stock is different (see below), check-in process is different, PNR is a different style, etc. It can be a little confusing, and the English isn't always great for the domestic check-in agents. So, I can imagine a lot of difficulty if you asked for through-checked baggage.
Personally I would go for it, you understand the risk of a mis-connect as your largest concern (very low). Just collect your bags at NRT and re-check.