I don't have a good answer for you but right now I'm facing a large diffused light that lightens my face and a backing green screen. Mine is floor standing and enormous, but you can get an equivalent diffuser attached to monitor and an LED behind that.
Building on this, I sit at a south facing window that gets good lighting for most of the day. I use a large circular photography light diffuser that can stay firm in the window frame using the tension of the diffuser. That plus slightly grainy background images to blend with the webcam footage and I blend well with any background :D
