Paper piecing in circles

I have been trying to work out how small of a circle I can work with for paper piecing. In the process, I came across a quilt-along at In Color Order to make a New York Beauty block. The block is about 16" on a side. The blog belongs to Jeni Baker, and she has either patience, precision or skills that I am totally lacking.

I made one of these blocks following her instructions...

and the quarters did not match up well - you can see that the points in the outer circle are narrower at the seams. But, it was a fun block to make, so I told my son I would make five more and see if I could end up with at least one good block. The second attempt...

is even worse than the first. The third showed some promise:

but is not flat - I think there is an issue in the center. Attempt number four:

has issues in the center ring of triangles where the quarters were joined. Number five:

still has issues with the center ring, but the colors seem to have worked out. The final attempt:

This is probably the best block in terms of alignment, but the center ring of triangles has a wonky triangle at the intersection of the top two quadrants. Maybe this will take five more tries to get right.