We have just moved and I'm 35weeks.
I think it depends on how your body copes with it all. I didn't do any heavy lifting just packing the boxes, unpacking and ordering the boys around LOL. But I didn't consider the stress and emotional toll. Lack of sleep because I was trying to help and not seem like a slob, and then the stress of "Aahhh!! my house is a wreck and I'm having a baby very soon!!!" There are a lot more triggers for stress when you are moving or just moved.
If I was to do it again, I would move at the late 20's mark (I think) as that was my least tired and before I got too uncomfortable and swolen.