I've watched Bonnie on QuiltCam and she sews inside the 1/4 inch line while piecing. She says this allows for the extra fabric needed to fold over the stitching line. I like Aurifil thread to reduce bulk at the stitching line. It sounds like you are sewing 2 triangles together so that the straight edges are on the outside? Using the larger squares, and sewing two lines down the center to get 2 half square triangle units should work just as well. You can then trim them to the size you need.
There are easier methods for doing some of her patterns if you are using yardage rather then scraps. Her methods work well to get the most from your scraps.