I've been watching videos on Bargello for current project. This video shows a guy using a "leader" piece of fabric before beginning the stitching of the strips in order to catch the threads. This works great! No loose threads everywhere-they're all attached to "leader"! (He starts sewing at about 7 1/2 minutes)
https://www.youtube.com/watch?v=yTsW80EANKI
It's probably not a new idea, but it's a new tip for me.