I've got it!
This is the triangle of the week for the Dear Jane list. (See my link on the right). Nancee's Fantasy looks difficult, but I think I found a way to avoid set-in seams, if you don't mind foundation paper piecing 7 sections.
I used to not like paper piecing - I found it so frustrating. BUT, on these small DJ blocks it helps me get the accuracy I want. I just cut my pieces of fabric extra large and trim after I sew. The extra time and effort is worth the saved frutration.
Anyhow: take a look at my photo above, and click on it to see the large image and the details. Thank you to whoever on the list mentioned straight diagonal lines - then my inspiration came! I changed a line through one small triangle (see above) The center lozenge has two pieces of background fabric added to the bottom ( I added a seam here). The heavier lines outline the separate sections - I hope you can understand them. Then add the thin vertical section that is like a frame - 3 pieces here, all numbered. Then add the outer parts. Then add the two bottom sections. Each bottom section has one large triangle of your focus fabric, background fabric, then a tiny triangle of focus fabric. I sacrificed the shape and size of this little triangle, but I thought it was worth it.
After this bottom part is done, add the two triangles of background fabric, and then you are ready to add the point, which is also paper pieced.
Now; I haven't actually cut my fabric and pieced this, so I don't know how it will work. I plan to print out at least two more outline images of the triangle and cut them up into paper piecing sections. I'll post images of my progress.
Hey, a PHD is science is something- it has improved my problem-solving skills!