I selected all my objects, then I did a "Lightmap Pack". Initially, it seemed like everything went ok. However, when I look closer, it seems to have stretched some the UVs.
The shape of the selected UV on the left, is not a match for its corresponding face on the right. Why couldn't it preserve the shape?
Update #1: I did more looking around, and noticed that the smallest faces seem to map correctly; notice how this tiny square face (from the same object as the big one) actually did the mapping correctly. I also (for sake of trying) did an "Apply Scale" to all my objects, it seems to have made no difference (even after re-doing the lightmap pack).
Update #2: Max'ing the "quality" setting for Lightmap Pack didn't seem to fix it, or even make it any less distorted.