Instead of multi-story pits. How about a raised pit? or split-level pit? Surely there isn't a FIRST rule stating that the pits must be on the ground right?
It would make getting the robot up there a little difficult but given the thoughts being tossed around, I'm sure someone can figure it out.
If you take a look at the picture, that cutout is for the robot cart and lifting mechanism. the space between the pit and floor will have no body parts, but instead, they will have buckets full of tools, parts, etc. The front of the pit (and side if you are lucky enough to get a corner) will have cabinets for storage purposes.