With the time just outside the IAAF requirement, Carson will need to either run faster than 3:36.20 or to wait to see if he gets an invite from the IAAF and his nomination confirmed by the NZOC.
Speakman finished sixth in 3:37.85 and had the satisfaction of smashing his previous best by 2.41 while getting close to the B standard time.
Matthews improves three places to seventh on the NZ All-time list for 1500m, while Carson moves up five places to ninth and Speakman joins the exclusive top 20 in the blue-ribbon event at number 14.
Carson, Matthews and Speakman have been training in Arizona and Michigan with Nick Willis [who was the rabbit in the Swarthmore race] and were targeting the race as an opportunity for securing qualifying times for the Rio Olympics.
Each country can have three athletes per athletics event and with Willis already selected, the competition is intense for the two remaining spots.
The next opportunity is a race this weekend in Windsor, Canada.