You can't SDC at the start of an international itinerary.

Have you looked at the prices for even earlier arrivals into LAX? In fact, would it be cost effective to fly to LAX the afternoon/evening before and stay in a cheap airport hotel to enjoy a bit of the LA area and relax? What about a redeye?

Have you checked the fares for flights into HND instead of NRT? They generally tend to be cheaper and more available if you can make the times work for you and you don't need onward connections from NRT.

If necessary, I'd pay the $115 to avoid worrying about a potential missed connection and waiting a day at LAX for the next flight.