On re-reading your op, I see you're question is really about the center. I'm guessing you're having a hard time getting it to lay flat.
There are a ton of tutorials out there but I this one for a pinwheel - scroll down to when she's sewing the 4 pieced squares into a block. I think that's Eleanor Burns' method.
A couple of other tricks I've used on Mariners Compasses where there tons of seams coming together at the center.
I cut the seam allowance about 1/8" from the half block. I just sort of "spooned" it out to alleviate some of the bulk.
Now, I NEVER hand piece, but the best trick I learned (I can't remember from where/whom) and use with machine piecing was this:
When you're sewing the quarter units into halves, and halves into the whole block, was to NOT sew the seam through to the end. Stop at the seam allowance and back stitch. When you finally sew the 2 halves together, you're left with a tiny whole in the center, but there is not bulk because you never sewed all those seams together.
Works great when you have 4 or more seams in each quarter. Try both methods with some scraps first.
Actually, I would think the second method is similar to hand-piecing where you sew over/under/through but not in the seam allowances