I've had to come up with a jig to keep the piece verticle and travelling straight due to the large gap in the router plate and fence. I also use one of those fancy yellow push block jigs for the other piece, to keep it square to the fence and stable. It's one of those Gripper things.
Here's a video that may help with the vertical jigs, etc. for alignment. These boxes are uncannily similar to what you guys are making.
https://www.youtube.com/watch?v=By1z-AI9PhU
http://lumberjocks.com/TheHarr/blog/30099