Well, consider the size of the graph. To get from the first scene to the transition to the bedroom takes 80 to 130 choices. Each scene has an average of about 2.1 exits, so we're talking about 2.1^80 to 2.1^130 possible paths. It takes the script between 0.5 to 1.1 seconds to process each playthrough.
I don't think the size of the graph is 2.1^130 (though that's an interesting bound), because every decision doesn't modify the *next* node in the graph; it only modifies the state vector "a bit", right? So calculating the graph is actually the interesting problem--what are the probabilities of each scene following a given scene? And do those match your desired probabilities? (And also: really? 1.1 seconds to traverse the graph once? Are you making http requests or just processing the files? Can you load the whole thing into memory and just traverse the graph in memory?) Drawing the state machine would be hard, but given that you have a way to traverse the thing pretty quickly, you should be able to build up a probability map of each scene's entries and exits. Looking for near-zeros should tell you if you have a problem or not.
It's an interesting problem, though.