I don’t have my Space Shuttle on legs at the moment but I don’t believe the playfield hinges operate in the same way as on that video. WPC games as shown do let you pull the playfield forward like that. You have a much earlier System 9 game. I believe they only have a single pivot point/plane back there so lift by the apron and it will pivot towards the backbox. You can use the prop rod to support or gently guide it against the backbox.

I like to respond to Pinball repair needed ads when I’m on Oahu. Haven’t really been taken up on the offer yet, though. Sadly, we just got back from a Caribbean vacation so no Oahu for us this year.