I believe that the only way to find this out for sure (SWU availability) is to call UA and ask. The problem with expert mode is that if there are not seats available for awards, they will not give you the other inventory numbers on that flight. There is certainly the possibility that award seats are not available but SWU upgrade space is available.

But almost every UA agent I have called about this availability is more than willing to look at as many dates and flights as I tell them, without making a reservation. And they even tell me if there are lots of seats available for upgrade, or only one or two.

And I suggest checking it and booking it segment-by-segment. For example, UA 881 ORD-BKK stops in NRT. However, there might be upgrade space available ORD-NRT but not NRT-BKK. If the reservation is booked as two seperate segments, you can confirm one and waitlist the other. If it is booked as a single flight (ORD-BKK), you would have to clear both flights before getting an advance reservation in business class using an upgrade.