This is correct.

There is no such thing as outbound or inbound in the *G rules. Access is granted only based on departures, not on arrivals. For a *G to have access you must have a *A boarding pass for the same day and the travel must be "travelling in conjunction with a Star Alliance international flight." That means same-day itinerary by most interpretations.

So if the EWR-HNL-NRT is all on the same day then the EWR access is granted by having a CO BP and for being in conjunction with the HNL-NRT flight. On the return it is the same idea. Access is granted in LAX based on departing the local airport on a *A flight and because it is in conjunction with the NRT-LAX flight.

If there is a stopover, even just overnight, you'll lose the access at EWR or LAX.