Thank you so much, this means a lot!
And you're pretty spot on with the random-roll mechanic. Interestingly enough, random rolling was originally going to be the only way you could change the cube's rotation, and let me tell you, that version of the game was... not fun. At this point, the random rolling is entirely optional, and really just there as a hail-Mary tactic for people who aren't as concerned with finding the "correct" solution (I'm a fan of people enjoying games their own way).
I'm still super interested in how randomization could be incorporated where it feels more integral to the process and adds to the fun rather than detracts from it. Hadn't quite cracked it by upload time; hence, this version where it is situational and non-essential.