Have you tried tucking the thread tails by hand? Leave a long thread tail rather than cutting close to the fabric, thread it onto a hand sewing needle. Run it back and forth between the layers a few times, then clip it right at the fabric surface. This works if there is a batting as there appears to be some sort of batting or interfacing in your photo. I've only done it a few times with monofilament thread so can't attest to how well it holds over time. Just a suggestion. I do it with my thread ends when machine quilting if I have to stop and start in the middle of a block because I can't stand having a knot or even any thread build-up. It does work great with cotton thread and batting.