Three thoughts come to mind. First, it's probably doable; as far as collecting the tickets at NRT I can't speak re Sundays, but it ought to be possible for you to have them held at the AA or CX desks there.

Second, almost everything intra-Asia from NRT goes through HKG, so you're really asking about longish-haul options from HKG in a short time frame. One possibility might be NRT-HKG-BOM-HKG, with a turnaround (wee hours) at BOM, returning to HKG in time to connect to a CX flight to LAX (this would be the 15th departing BOM & HKG and arriving LAX.) Many hours in tubes. BOM is one of the longer segments from HKG (stops at BKK but same flight no. so one coupon.) That would give you two days to get to ORD and then ACA. Whether that's a good use of your coupons is your call.

However the third thought is that before you're likely to finish your RTW, JAL may well be in the alliance and bookable on OWEs, so a re-issue might increase your mileage yield substantially, since JAL has several very long intra-Asia segments (NRT- DEL/DPS/SIN for example.) That might be my first choice - go to NRT, pick up your ticket, fly straight back to ORD, and save the Asia segments for later, when they might go farther due to JAL's joining. Easier on the system, too - no need to worry about resetting your clock.