Don't be frustrated! I think you're probably making it seem more difficult because it's such an important quilt for a special person.
Here's how I would do it:
Cut 14 (6 1/2" wide) strips. From strips, cut 84 6 1/2" squares. Cut them once diagonally to make your half square triangles. Pair them up and sew them together.
Your resulting triangle squares will be just a smidge larger than they are supposed to be. The pattern is using 5 1/2" finished triangle squares, so you need to trim these to 6" square and they'll be ready to use.
Someone else should double check me, but that's how I read it.
Take care, Onalee. I'll keep good thoughts for you and your brother.