A large part of the problem is that you are essentially using only a single, relatively hard (small and non-diffused) light source. That sort of lighting can create very dramatic pictures, but not of the sort you are trying to shoot here. You want colour across most of the petals and leaves, but the only light the bulk of the flower is getting is reflections from walls and a ceiling that are too far away in relation to the main source. That, in turn, means that specular highlights are going to blow out long before the "body colour" is established. To expose properly for the highlights (as very high highlights) under those conditions, the flowers themselves will be extremely dark. Dramatic, but more in a filme noire sort of way rather than a textured flowers sort of way, and that's probably not what you want.

The only change you need to make, really, is to put a large-ish reflector just about where the camera is in your setup. (Above the camera, of course, not in place of the camera.) A couple-three-four square feet of white fomecore will work wonders, pumping enough light into the scene that the highlights will be much lower in value compared to the main values of the flower and foliage. It will not be strong enough or hard enough in relation to the main light to create cross-reflections or any other obvious "I stuck a light there" artifacts, so you'll still get dramatic textures and deep shadows. The only change will be that your highlights and the rest of the image will fit into the same exposure.