I was on SWC 3/9-3/11. It was simply first come, first served. After walking the sleepers, the LSA made an announcement for any sleeper passengers who had been missed to come to the diner to make reservations (she did not check the SSL for sleeper passengers.) A little while later, she made an announcement for any coach passengers wanting diner meals to come to the diner immediately to make a reservation for a VERY LIMITED number of available slots.
I spent all of my time in the SSL, and on one meal I went to the diner to make my reservation, and before I left, a coach passenger came in and asked for 3 dinner reservations. The LSA said, "OK, that's it then, I have no more available." So apparently, it wasn't a hard number 16, but whatever was left after sleepers, in this case just 3.