The plan is that on the first day of class, I'll distribute name badges to each student and have them write their names on the badges (I'm thinking of semi-permanent name badges rather than simply stickers). I'd collect the badges at the end of each class. When the next class meets, I then randomly place the badges on desks in the classroom, thus gently suggesting where students should sit. I'd plan to do this before each class meeting.
Well, I've got an update: I'm trying this in my larger Gen Ed classes, and I am definitely learning the names a lot quicker. I've not yet collected and redistributed the name badges, and I've not yet decided if I want to do that. I did add one wrinkle I like a lot: I gave the students plastic sleeve-type badge holders, along with one of my university-issued business cards. They then wrote their names on the blank side of the cards and put the cards in the sleeves, giving them a name badge and a handy reference with my contact information. In any event, the student reaction to this has been very positive.