We actually did have to cut some deeper puzzle mechanics and additional levels. We originally wanted some side effects to "conflict" with each other and not present if they were combined in the same subject, making things significantly trickier.
100% agree with it having been better to be able to guess the answers in any order you want. We tried, but there just wasn't enough time to implement that, even though it would only be slightly more sophisticated than what we have. We went right down to the wire on this one.
Thanks so much for the thoughtful comment!