I know you say that the desk puzzle isn't broken but I got a result that would have been the same for 2 demons and blocked me from continuing so I had to restart.
So I checked the code and this shouldn't be a problem. Can you describe the exact situation you had? Since you draw the sigil first, you will be locked into whichever demon you drew the sigil for. So even if all four demons had the same chant, you will get that one since it's locked in after the sigil drawing. I'd need to know your exact situation to troubleshoot this. Thanks, again.
305 days ago (+1)
I'm afraid I can't remember it entirely but I was going for the Devil and the paper sequence was:
[7] [8]
[8] [7]
and I think the pattern was: 
This was also on my very first run