Built a huge mansion on top of my base over the huge open room (though all closed up to make placing things on top easier). Finally decided to start working on the "sub-basements", opened the huge room up (apply to base from entrance room), then tried to fill in individual sections to create the walls for the rooms I wanted. Took FOREVER to get it to select the room section and not some item on top of it.
The trick I found to get it to work easier (still took a LOT of patience) was to get as close to the floor as possible and move along the "seam", I guess you can call it, clicking right on the edge of the floor tile section. Sometimes this would work for several sections in a row, other times it would take several minutes each of sliding around on the floor clicking.
Still think it came out pretty well, so far, for my first base build since playing live (which was WAY more restrictive).