My first half square quilt and I keep breaking thread on thick areas

I’ve made a few simpler quilts and I wanted to challenge myself with a chevron pattern out of half squares. Included lots of pictures in case it will help, the thread keeps breaking only when trying to sew the thick part where all the triangle corners meet. It’s like the needle can punch through but the fabric is so tight it doesn’t allow the thread to come back out without breaking. I’m using an old kenmore machine from the 90s and I have it on auto tension.

I’m at a loss of what to do, it’s really hindering my progress. Any tips?