So here's what I came up with.
Step 1. I separated embroidery thread into two sections and then took one length of thread and thinned it down to a few strands so it would fit through the beads.
Step 2: I threaded the thinned strand onto a needle and strung 6 of the mother of pearl beads, knotting it at each end.
Step 3: Take one of the sections of embroidery thread and wrap a piece of scotch tape around the end so it's almost like a shoelace and can go through the rectangles easily.
Step 5: Do the same thing with the other strand, but weave the opposite way. Knot the two sections of thread on each end. Don't pull too tight or the beads will start to bend upwards and zig-zag. Combine the 2 strands and then separate them into three equal sections.
Step 7: Knot the end with a toggle clasp inside. I affixed my knots with a little bit of epoxy glue to make sure they hold up.