M-3

I wanted to name this post "Woo-hoo!" but since I have a naming convention...
I finished "the block". The hard one. The one I simply could not figure out.
What follows is what I did and not necessarily the best method.

One thing I know: try to sew as accurately as possible. Even the teeniest misstep can result in big problems.

Print or trace the block diagram onto foundation paper, number, and cut out the sections as below.

If you're using freezer paper for foundation piecing keep the "frame" part of the block diagram intact, else trace or print the block diagram onto the dull side of freezer paper and cut out the "frame".

Foundation piece the three sections and trim the seam allowances to 1/4".
Don't worry about the sharp points of the sections. They aren't going to show.

Sew the three sections together.

Mark the four kite sections on main block fabric.  NOTE that they're not symmetrical. Take note of which side will face the center of the block.
Cut the kite sections out only along the two seams that face toward the center of the block.  Leave ample fabric on the other sides (at least 1/2" beyond the seam lines of the kite).
Sew the four sections into the appropriate areas on the block.
Sew only the two "inside" seams.
Yes, you will have to use set in seams.  (Sorry.)

Cut four 4" squares out of background fabric.
Use these to make four half square triangles.
Sew them together as if you're making a pinwheel.

Iron the freezer paper frame you made in the beginning to the right side of the block, lining up the seam lines.
Cut out the center section, leaving a scant 1/4" seam allowances. Clip the inside corners. (Actually you can just unpick the seams up to the freezer paper edge.)
Place the foundation pieced block section right side up on the table.
Place the "frame" section right side up on top of it, carefully centering it.
Baste through all layers at least 1/4" away from the freezer paper frame edge.

Turning under the seam allowances, reverse applique the "frame" to the block center.

Trim the block to 5" x 5", i.e. 1/4" beyond the freezer paper edge on all sides. Remove the freezer paper.

Cut away any excess fabric from the back of the block.

Press.

Woo-hoo!