I would piece the diamonds in 3 units, with seams here, this way it could be strip pieced and just cut the 45 degree ends
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I would treat it as almost a dresden plate. It is 8 points so I would start w/ a 45' diamond, take off 1/2 inch from each side of 4 of them and add that to the alternate 4 (accounting for seam allowance). Fold over the outer seam allowance sew the diamonds together then machine applique to a background square and applique your square center to the whole thing. (I would remove the 8 point bulky center before placing the center square.)