Woot! The contractors came out today to fix the shower drain. First they had to find the blame thing, and - after digging down about three feet in a rough estimate of where it would be, they found the line. After cutting out a piece, it was pretty obvious that the drain problem was due to ... [drum roll] ... lime buildup. They ran a
jetter along a pencil-line (i.e., a thinner line), because it was needed to enter a 1-1/2" pipe.

After jetting out the calcium build-up, the pipe was cleaned out, and all that was needed was a coupling to repair the cut section, and then I had a perfectly draining shower.

Luckily, we now know where the line is located (and a good idea where the drainage cistern is located, too), which will mean that it will make it easier to take care of similar problems that may arise in the future.