Disclaimer- I'm not speaking from experience. I'm just making an educated guess!
I would approach this by thinking of rows rather than stars. Looking at the bottom row, you can make units using the hexie, the upper right triangle, and the lower left triangle. Once the triangles are attached to opposite sides you'll have a diamond shape. When all the diamonds are made you only have to sew straight seams to put them together into rows. The lower left triangle becomes the lower right triangle of the hexie to the left, so there's no need to add the triangles around each hexie and mess with Y seams. For this to work, though, you need to be consistent with the triangles you add - always use upper right and lower left or upper left and lower right.
I hope this makes sense! I can see it in my mind's eye, but I'm not sure I'm getting a good description here.