If it were me I would tend to think in terms of creating a larger light source from your single strobe. I have done this in the past by making a "bank" out of white rip stop nylon. I have used this both by shooting the strobe through a single layer of rip stop and also by reflecting the strobe off a double layer of rip stop. The distance that the strobe is positioned from the panel is important since that determines the size of your newly created light source. My bank was on the order of 3 by 6 feet as I recall. A frame can be contructed from 3/4 or 1 inch PVC pipe, elbows, and tees. The rip stop can be afixed to this frame with spring clamps or even duct tape if you are so inclined.
To have your object "float" on the green surface...if the material is flexible, create a transition much as a transition table does it by not having any sharp corners at any point but rather curves from the horizontal to vertical transition.