I had my baby shower at about 32 weeks I think. It was good because I was very visibly pregnant but not so huge that I was really miserable. I can't imagine dealing with all that later.
I have slept my baby on her back since birth and she is now 8 months and doesn't have any sign of a flat head. Yes it can happen but it isn't a given, and as others have pointed out it will fix itself anyway. I could never live with myself if something happened to her and I hadn't done all I could to prevent it.
But ultimately just like breast vs bottle, starting solids etc it's your decision.