There are no HSTs in that block as designed. A lemoyne star (the center building block) is not built on right angle triangles, it is 45 degree diamonds. Changing to HSTs will give a similar look, but is not the same block.
I see two options with this design - accept the mutitude of Y-seams (they really aren't that bad) or split the squares, and the triangles on the edges so they have a seam line down the middle.
If you stick with the pieces as drawn, I would assemble this in quarters. First, the upper left - a center square surrounded by 4 diamonds, then add the two brown triangles. Then add the next sides - the red/green diamonds and the yellow/pink diamonds. Make 4 of those. Join , and use y-seams to add the 4 triangles that connect these quadrants.