Thank you all so much for all your suggestions on how to be more successful with making this block. There are so many ways to get to a good result:  make half square triangles instead of sewing triangles to the square, hand piece the block, paper piece the block and more.  For me though, it all boiled down to two things, which in my heart, I know to be right:
1)  Starch the fabric
2)  Make the units larger than called for, then trim them down to the correct size

There was also a fair amount of operator error in my technique with the Creative Grids ruler.  There are several places where one is supposed to trim with the tool.  It turns out, I was neglecting to do the final trim down of the "Cat's Cradle" unit.  When making the units the specified size, this trim amount was negligible, but when I tried making the units slightly oversized, I could trim off a good amount and ended up with perfectly square units.

Here are some photos I took when making my test block in red and cream:

I made my units a quarter inch larger than I needed.  When the pieces were sewn, I used the Creative Grids Cat's Cradle tool to trim them down. You line up the solid lines to the size you want your square, and the diagonal lines to the size you want your finished unit.  In my case, this was the 2 1/2" diagonal line.

Trim two sides, then flip the block and trim the remaining two sides. You will end up with a perfectly square 2 1/2" square unit.  (There are other size options on the tool, I just needed 2 1/2" for my blocks).

Lay out your block units and stitch together.

Here is my perfect red block next to my sad floppy blue block from yesterday.

I had also gotten away from starching my fabrics prior to a project, which is really not a good idea.  Always take the time to do that, you will be much happier with the results.

Besides listening to all your great suggestions on how to make this block better, I did watch two YouTube tutorials.  One was by Deb Tucker, who invented a trim tool (the Tucker Trimmer) for this block, which is practically the same as the Creative Grids ruler.  I watched her instructions, and she is so clear and concise, I immediately grasped what I needed to do.  Then I watched another tutorial, specifically for the Creative Grids tool, but not sponsored by that company.  These two funny gals from Prairie Quilt started out bickering over what their favorite Thanksgiving menu item was, but then got into a demo of how to use the Creative Grids tool, which was very instructive.  You should watch it, they are pretty funny.  And their demo was more clear than the one Creative Grids put out to sell their ruler.

Thanks again to those of you who took the time to make suggestions.  I really appreciate it!