I think putting the answers in random order may have the opposite effect from what you intended. It means the user has to find some other way to keep track of what he has already guessed, and the easiest way to do that is to make his guesses in alphabetical order. That naturally leads to random guessing (saa, sab, sac, sad, . . .), and there's enough time to go through all the sa_, se_, si_, so_, and su_ combinations and then double back and do s_vowel words to catch everything else (with 1:52 to spare).
I agree. I wouldn't say it has the opposite effect from what is intended, in fact I'd say it shifts things a little towards what we do intend, but not by much. Apart from requiring quizzers to wipe their brains clean after typing each word, I'm not sure what the solution would be. For now, it looks like you're the only person to have gotten every word, so it looks like there's still enough challenge left here for most people.