I'm not sure why CD wouldn't let me attach a file to a post on this thread, but I've posted my solutions to the cube at this "white paper":
https://www.chiefdelphi.com/media/papers/3289.
For any who find this white paper a bit too much, let me simply note here that you don't want to see all of my blind alleys and solutions which worked but were much uglier than what I've shown here.
Edit: And OBTW, if anyone feels that my substitutions showed a bit too much prescience, that's ok, because I'm posting this on my birthday, and we should always expect prescience on our birthdays, no?