I can understand your dilemma Twisted Quilter. When dealing with various size of blocks from a block swap, I had to improvised to get them to all work together. I found that attaching over sized triangles on all four sides and then after pressing, then trim them all down to one size. You can't use a star because the block has to be divisible by four. The center of a star block is the same size as the two side pieces.
This is what the block looks like and this is what the quilt would look like to scale of 4.25" finished blocks...... NOTE this was drawn on EQ5....