I borrowed one of my daughters hair clips to demonstrate a way to hold your thread ends. They do come in smaller sizes than this, but this is all I had to work with. You open them by pushing the middle. And close them by pushing them down.
This is my second attempt at the Glass Mat. It went smoother this time, but I still mess up. I need to apply lots of concentration to this and that's not always available. I did find a better way to take out rings, so that helps.