I haven't photographed anything this large, but I have had similar issues with the background and lighting when taking photos of some of my MOCs in the past.
If you can diffuse the light with something like a thin sheet or thin paper, that will help soften the shadows. I've also had some success with photographing outdoors on a cloudy day. I always find a longer exposure at a low iso is preferred if your lighting is not bright enough.
It's hard to get a perfectly clean and wrinkle free backdrop. Most of the time I Photoshop my backdrops to look as clean as possible. In some cases I've even completely cropped the background out using Photoshop. For example, my Bastion was photographed outside against some pieces of printer paper I taped together. The background was just an loose approximation of a completely white background, so I Photoshopped it out completely: LEGO Nanaimo Bastion
In general, I would say photo editing with Photoshop or something similar (maybe GIMP) is a must if you want to really make your photos clean and have balanced lighting/colour. I've also found shooting in RAW allows for the most flexibility in editing, especially in regards to adjusting colour balance.