Perhaps the groove you cut for the 'wire' is too wide (thick). I use hack-saw blades ground down to the width and thickness I want. I usually punch in about 3/32" deep. I cut my ribbons 1/16" wide or maybe just a few thou wider. I file a taper to the ribbons against a piece of wood, to create a knife edge section. I drag the ribbon between a file and a piece of wood to cut longitudinal lines into the ribbon which help to anchor the ribbon in the wood. After the ribbon is set into the groove, I use a wet cloth to dampen the wood and swell the groove shut onto the ribbon.
Alternatively, I use the ribbon at its full thickness, but lay it on a block of wood and with a sharp knife create a ka-zillion little knicks in the bottom edge of the ribbon. Many of these knicks will be displaced metal that sticks out the side of the ribbon's thickness, and once tapped into the tight groove and swollen, the ribbon can not come back out.
So, cut your ribbons narrower, ie: around 1/16" rather than 3/32". The narrower ribbons will seat into the groove more easily without folding over, which is another problem, especially with very thin stock.
