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Well, my hexy star block hasn't been perfected just yet, but I have achieved a 12.5", non-wobbly, non-disaster. I used smaller diamonds, to start with, and that put me on the right track for creating the "offset" look I'd envisioned - it's really hard to offset something that takes up most of the block.
Consulting the tutorial over at Sew Lux was definitely helpful - our hexes weren't the same size, so I had to augment with some extra triangles, but it was definitely a start. Her suggestion to add border strips on opposite sides of the hex turned out to be particularly effective in not stretching out all of my careful hand-piecing.
Now I'm wrestling with whether or not I should continue to wing it when piecing the outer borders, or just be responsible and make some freezer paper templates.
Decisions, decisions.