The pull out card is usually used for placing catch-lights in eyes when the ambient light is good.
You can, rather than use +5, which is implemented in the camera by slowing the shutter down, increase ISO, but it would have to be close to ISO 1000. The risk is noise, the potential benefit is that you can have better control of thew overall exposure by closing or opening the aperture.
Since you have essentially two main issues, light, and space, you have to make some decisions.
Think about natural, window light, - good diffuse light that has no direct sun; Then have the model sit, and use a longer focal length, concentrating on a head and bust shot. The chances are you will discover way more creative poses, and better results. So think about NOT moving back, but moving in closer with a 50mm focal length for example.
I did take many liberties with the mod, as you can see. I did make the lower hand and arm smaller; I evened out the exposure so its about the same all over, rather than bright and a lot less bright; Its rotated, - its an entirely different look of course, but you see it also can work if shes not lying down!. It also shows that when lying down, her face is pulled towards the floor, or, pushed by a cushion, it clear when its rotated.
Just some ideas.