There is one featured in the Woodsmith magazine, Vol 31/No 182 that shows the divider being dadoed into the ends and screwed from the bottom.
Another variation is in 'The Woodwrights Apprentice' by none other than Roy Underhill being used as a tool tray. But the divider does not go all the way to the bottom. In it he uses a notch/"mortice" in the end, (square hole in the end panels), the divider has the 'tenon' on the bottom portion. But the wood used here is thicker than I think you're planning to use.
Good luck.
robert