When I am designing in a tall square or cylinder style vase, I am a big fan of using natural birch branches rather than taping a grid to hold flowers in place. I cut the branches so that some of the "twiginess" (is that a word?) goes down in the mouth of the vase as an armiture, than I insert my other materials, usually greenery first then flowers into the branches, and they stay right where I put them, eliminating the need to tape things. When I do this, my twigs stand tall and become signifigant to the arrangement as well, not just as an armiture.
In design school, my instructor was always preaching that we use AT LEAST 3 types of foliage in all designs to add visual interest, and the only way I use leatherleaf anymore is just to cover any tiny holes that show my foam at the very end of my arrangement, never as a main greenery.
For a typical rose vase, I start with a branchy piece of something like boxwood, oregonia or bonsai eucalyptus right in the center of the vase to branch out all around. After that, I put in 2 tiki fern, to again fill the middle of the vase, and finish with a couple of salal leaves to the sides and a long pointed piece of plumosa coming out of the left front of the vase with a sweeping motion. This creates a pretty tight mesh in which to insert your flowers, and I have very little trouble getting things to stay right where I placed them.
I look at the placement of all my foliages just like I would place flowers in an arrangement. If your arrangement was a picture you were painting, each brush stroke represents an insertion, and you have to see it as a work of art, so every leaf or flower is important to the overall design.