Thank you for the nice comments. I did a small tute on inset seams, with the triangle in mind, that might help, and Abbey's eye is similar, though I had a couple of little wrinkles at the corners of the eye. I find that judicious use of a steam iron gets rid of most of them. I haven't starched any of my fabrics before using them, so I don't know how these inset seams would work with very starched fabric - you might want to try a small sample from scraps before you use your good fabric.
With Abbey's eye, I put the iris of the eye into the middle of the two background pieces, using the inset seams technique, then added the outside sections using the Y seams technique that Cutie did a tute on. Basically it's the same as the inset seam one, but instead of snipping into the corner to get around it, you just undo a few of the stitches of the seam so that it will open up for you. When you get to the middle, put your needle down, and fold as much of the bulk out of the way so that you can pull both pieces of fabric into line and stitch them. Hope that helps.