Good to hear you are working on the visa. Every once in a while, somebody comes on here that doesn't realize that necessary step. Currently, 10-year visas seem to be the norm. Do check that box, as the price is the same for that as a shorter one.
Are you using ITA Matrix to search?
Matrix - ITA Software by Google It will show most of the airlines doing the trip, and help you to spot certain days and routings that are priced better. Particularly if you use the month-long feature or specific dates + or - 2 days. Much more efficient for the early rough cuts at a trip.
Kayak and Google Flight are also good general swipes, although not as powerful as ITA Matrix.
In your calculations, including the value of miles can make a difference. Salt Lake City, Utah to/from Beijing is ~12,000 miles. Business class can be 50% or even 100% more, depending on all sorts of things. At a penny a mile, that is roughly $180-$240 per ticket. The odder the OTA, the less likely you'll also get the miles.
Not a huge factor, but buying the ticket directly from the airline with one of their credit cards can yield another mile per $, or $30 on a $3,000 ticket.