you do not need to remove the body from the the trigger frame or remove the solenoid in order to remove the ASA. you are correct about the board...it will need to be removed. disconnect the wiring harnesses first, so you dont accidentally damage them.
once you disconnect the wiring harnesses and remove the board, there are 2 screws inside at the bottom of the trigger frame. those screws are holding the ASA in place. those are the screws that are loose.