as you describe it's impossible, but I'm not sure what the DS relay is on that game or even what type of relay it is.
I don't have a sing along schem handy, but I'm going to the pacific pinball museum monday night and can look at a schem and at their working game to see what is supposed to happen.
turning on the game with the score motor out of an index position to try and force switches to toggle out of their normal sequence is definitely cheating