ORIGINAL: buzzard bait
...Using the middle of half the wing will put the CG further back than 1/3. Why would you do that?...
You are incorrect. The accepted convention is no more than a 1/3 back. 1/3 back of what?
Ans: The MAC. You could have a cg more than 1/3 back at the root, but not at the MAC. Beginners can start to understand where some of our "rules of thumb" come from. It is more accurate to measure 1/3 back at the MAC and then relate this location in reference to the root. Obviously a constant chord non swept wing won't have a difference.
Kurt