I don't use United.com for anything in my searches. There is something funny about what United has for avail award space on their metal especially and what ANA can see and when. My process from scratch usually goes like this:
- Use Google flights one way explore destinations map with nonstop and star alliance only checked. This gives me some idea of the direct flights that exist from any departure city that could be tied to a ANA award.
- Then I use Expertflyer (i have basic subscription) to search that airline and route for one ticket only for a 7 day span and "direct nonstop" connection preference. When results come up add filter out to show available only.
- If I find something as available I jump to ANA website, use award booking, multiple cites and put in what I found on Expertflyer PLUS a misc entry after that date for the search to work. If it shows up there the ANA agent should be able to see it. Generally I run it for one ticket first and then update it to two etc. For your trip there is actually ONE ticket from NRT-ORD in business on 6/7 but only one. If for example you could have found one on the 7th and one on the 8th it might be worth splitting up for a day of travel. We had to do this with 3 people traveling. We found a great set for two of us and then I flew out separate on another day.

I like the thought of Japan first then to ICN then home. Good chance you can find the flights to do that and saves you a hop back. I think ICN-ORD for two seats was available 3 days that week.

Good luck.