If you can move the lower tie from the edge about an inch along the back and tie it to the tailpiece cable, that will put the quiver onto the bottom of the tailpiece. You could do this by making two small holes and running the lace through. That little change will anchor the quiver very well and it won't move because the edge is tight against the front of the tailpiece. I use simple leather latigo lace which is like leather boot lacing and square knots, sometimes tying a double knot. I've made several quivers and these things have worked well for me.
YMMV, TEHO, etc...............
You forget sometimes that you are playing music, not just playing jazz. ....Charlie Haden