Your greenery is meant to frame the flower designs. Having too long of stems (or too big) is a common mistake. Just because the greens come with lots of laterals doesn't mean they should all be jammed into the design.
I insert from the sides, gently inserting the stems between the natural grid formed by the flower stems.
You can see the natural curve of the leather leaf is used to the advantage, and that the length is proportion to the height of the flower heads.
If you cut off laterals, set them aside for insertion into the center of the vase later.
Insertions from the side should surround all the flowers. Turn the vase to keep the placements even.
The greens should curve down naturally, with no leaves going below the water line.