As to how it fits into the case, all the header connections are brought to the edge of the OSPi board so a tall header can be used to attach a board and put it above the Pi. Adafruit has a LCD with push buttons for the Pi that will work. And a tall case is easy to do now that the case is laser cut (if you have access to a laser…).
There are some postings about similar things that might help you if you are able to do some code hacking. I am looking into that myself.
Was only able to find one that has available code.
https://opensprinkler.com/forums/topic/ospi-with-lcd-and-push-buttons/