I assume your last piece - 2 3/4 x 6 1/2 I cut 3 x 6 3/4 - is supposed to go right across the quilt. There's your problem. A 6 1/2" finished square needs a 7" piece to make the length.
I'm trying to piece together your puzzle (pun intended
) from your description and some photos. I believe you have 2 A's, 1 B for the center strip, and 2 C's for each end, right? The pieces you mention actually make a 6 1/2 (unfinished) square. So I'm confused on what you want.
If you really want 6 1/2 finished, then you need a 7" unfinished square. You need to cut:
2 1/4 x 2 1/4. (Piece A)
2 1/4 x 4. (Piece B)
2 7/8 x 7. (Piece C)