It may help if you have a candid chat with your captain and work on specific skills that will reduce your anxiety (eg. riding in traffic or group, start/stop, tight turns).

You can accelerate your learning process by riding with more experienced teams. Since you live in Seattle, have you considered joining the Evergreen Tandem Club on their regular rides?

Seattle also has several tandem dealers. They may do a tandem fit to improve comfort and efficiency (eg. wider bars, proper reach & stack). What works on a single bike doesn't always work on a tandem. They can also suggest upgrades that are compatible with your Burley.