Assuming you are hand quilting. I can't get through that many layers without stab stitching or taking one stitch at a time with a back stitch.
Another option is do the 1/4" away but not in every diamond, just inside the peremeter of each star and again around the outside edge and on the middle white diamonds I would have to think about it after getting the other parts quilted. The center whites that form that snowflake shape may need no quilting at all.
PS your block is beautiful and impeccably pieced. Is this for a QAYG project?