If your material won't need ironing you could use invisible thread and sew just the top and bottom. If it will need ironing you'd have to remember not to iron the thread because it will melt.

Maybe run a tiny line or dots of fabric glue to hold down the tips. FabriTac is one brand as is the Ailenes brand.
That would help hold those pesky tips in place.

Wide zigzag stitch that is really long so it stitches into the points of the rickrack?

If you pre-shrink the rick-rack, it should lie flat after washing.