I was thinking of using a connector header rather than solder the LCD directly to the board. It would result in an 11.1 mm board-to-board gap rather than the 2mm gap if I solder directly. I'm thinking the flexibility would be worth the lost space.
I'll need to use standoffs to support it if I do.
Felix, can you please tell me the size plastic screw you include in the kit (#4-40, #6-32, #8-32) so that I can order some standoffs and screws that are the same size? One corner of the LCD looks like it shares a hole with the four mounting standoffs while the other three are unused.