Setting pieced blocks with Snowball blocks (where the corners of a square are triangles) is fast and fun and has all sorts of possibilities. You can do a google on Snowball Quilts and get a 1000 ideas.
For best results the triangles of the Snowballs should match the triangles or at least corners of the pieced blocks... for example I'm going to be using some large scale Easter print as the center of my Snowball, and have decided on a LeMoyne star in coordinating colors with an extra triangle on the corner blocks. Or, in your case you can use the large piece for embroidering. The alternating blocks can be anything you want, from 9/16-patches (you said no squares though) to Churn Dash or Stars or really anything.