I think you’re on to something. I’ve also got Sunbird and at first I had about the same numbers as Matt: each added instance of Sunbird only increased the project file size with some 300 kB and I didn't have any slow save operations. The Sunbird version installed was 1.0, visible when scrolling to the bottom when the Display Window button is pressed in UVI Workstation.
So I went to my Acousticsamples account and noticed that there was a version of Sunbird available with a time stamp of March 28 2017. I knew my installation of Sunbird was older than that so I downloaded this new version and installed it. Strangely this release was also labelled 1.0 in UVI Workstation, but the file size had increased from 1,601,335 kB to 1,605,306 kB.
And now with only one instance of Sunbird in the project, the project file size jumped from 403 kB to a whopping 13,002 kB. And inserting a second instance of Sunbird made the .cwp file jump to 25,806 kB.
Something has definitely been changed in this Sunbird update. I think the quick answer to your problem is to reinstall the next to last version of Sunbird. I know I will until further notice.
BTW: I noticed in my account that both GD-6 Acoustic Guitar V2 and Telematic V3 had the exact same time stamp: March 28 2017. I wouldn't be surprised if they all share the same problem.