Remove Greenscreen Reflections?
You don't say what you're using to edit these videos, but there may be a better chromakey plugin for your platform than what comes natively. 

Also, again depending on your platform, most editors will allow you to crop the key area (garbage matte) so that the green screen doesn't have to cover the entire raster, just enough to back the product you're shooting, so you could put the screen as far away as you like.