Starch, Starch & more Starch. Diamonds are as tricky as triangles. Try not to handle the bias edges overly much and do not tug on them!
Except for the setting triangles, you could cut all these as squares--even the sashing & cornerstones, I believe, and use a diagonal set. It's very close to your diamonds but no bias edges to deal with. I'm attaching a photo.
Diagonal set squares instead of diamonds
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