Raspberry Pita project, lesson learned #1: The Pi3A+ gpio header is a nightmare to desolder, and if you do manage to desolder it, you'll probably also desolder components you don't want to and fry the board. Instead of plugging the button board into the back of the Pi, figure out how to redesign it so the button board plugs into the front of the Pi. This means the board will need many, many more slots cut in it so the various jacks can be accessible. Bonus, SD card should be accessible now.
An instance for Kazriko