I am working on a quilt that has over 2500 pieces and I broke it down into batches. I cut the fabric for 12 blocks at a time, made the blocks, then did the next 12, etc. for the 48 blocks.
Facing cutting out that many pieces is a daunting task! I'd break it down into parts or sections.
I just looked at the Buckeye Beauty link and realized that I was looking at one in the Connecting Threads catalog tonight. I would do strip piecing with that, like a strip of white sewn to a strip of blue, then cut them into sections to make the blue/white squares and sew two sections together for the 4-patch block. Of course, if you're doing all different fabrics/scraps then that wouldn't work.