Do you have enough fabric to test sewing on a sandwich?
I broke many needles sewing several layers where the half square triangles met in my blocks. It wasn't the pattern you are sewing but it created the condition you are speaking aboout.
Good luck.
Regards, Dorothy

If you break needles sewing through the thickness of layers, try using a 90 or 100 size blue jean needle. I alter a lot of jeans for folks, so that's what I had to go to using on them. Good luck.