I think Maryanne Fonz calls them spiders. I used to use "leaders & enders" when piecing to eliminate this same issue. Then, Bonnie um, total halfsimers moment...Hunter? Huntsville quilt lady made this stunning scrap quilt. All she did was start and end each chain piecing with stitching together a couple small squares. It served the purpose of eliminating the spit up and at the same time creates pretty blocks to use in a stashbusting quilt someday.
She has a few ideas. Google her website, or it's on here somewhere.