If it's not a commercial location:
What I do when building these things (and I've built a lot) is this. Wire the Test button wire to the 2nd button. Wire the Service button wire to the Player 2 Start button.
Now you won't have to open the coin door at all. Just hold the 2nd button down (the 1st button is the normal fire button for Galaga) when powering up and you'll boot into the Test screen. Hold the Player 2 Start button down and you'll boot to the Service screen.
Then when you do any programming changes, you can hit the 2nd button to advance through the screens, the Player 2 Start to go back, the 1st button to make changes, and the Player 1 Start button to save. Everything is right there to do whatever you need without having to keep bending down to push a button inside the coin door to advance to the next screen.
Also, during normal menu and gameplay screens, those double-wired buttons will only work as they are intended. the Test and Service aspect only applies if held down during power up.
And I said for non-commercial, because if you have it set for coin play, the Player 2 Start/Service button will act as a credit button....