Thanks everyone for the suggestions!! I'm working with heavyweight polypropelene webbing, both sides wrapped in cotton fabric, with one of the pieces interfaced. It is VERY thick and difficult to sew through. Hand-sewing is probably out, but I like the idea of back tacking (if I can get it to look right aesthetically. I will definitely shop around to see what I can find by way of fabric glue.
I should also add that I tried Sulky polyester invisible and hated it! It was always snapping or jamming up in the bobbin. It's likely due to my error, though. I believe the tension has to be adjusted.