Answering my own question about FLL as I went through it today. At T3 they had three lanes crammed into the CP area. It was very crowded and they were herding people through. We ended up in the right lane that had both WTMD and the BKSX. The middle lane only had a WTMD and it MIGHT be possible to preselect this lane but we were't able to since it was so crowded we were herded into the other line.

But for some unknown reason we lucked out. They only sent some people into the BkSX and told others (us!) just to go to the WTMD. I saw no rhyme or reason to their decisions.