I managed to fix the issue..no thanks to Apple. I have no idea if this will work for anyone else, and I obviously take no responsibility for any of my own actions should you choose to follow them. My working theory was that if I could get a device to allow me to reset my end-to-end, I might make it out of the loop.
Big Sur would never give me the option to reset my data, so I figured I might as well try something stupid. I was at the point I didn't give a damn if I lost all of my messages and passwords.
Here's what I did:
1) Drank whiskey (may or may not help)
2) Wiped my laptop and my phone, and ensured both were removed from my account through appleid.apple.com
3) Downgraded my MacBook Pro to Catalina (fresh install through internet recovery) and signed into iCloud during setup
4) Same issue presented itself, so I continued to smash that Keychain button
5) Went on an endless aggravating loop of entering passwords over and over again--but it was at least consistently asking me to enter passwords in a predictable and repetitive fashion (unlike on my iPhone and Big Sur).
6) Drank more whiskey
7) Eventually, out of sheer aggravation, hit "Forgot Password" on the "third" password request (the one protecting your encrypted data) and I was finally presented with the option to "approve from other device" (there were none LOL). Forget that mess. Some more clicking around, and I had the option to reset my encrypted data. I smashed that reset button and watched as my computer locked up and crashed. Repeated several times and it finally went through.
8) Laptop appeared to be syncing with keychain, messages, etc. Several minutes of disbelief that something so dumb would/could actually work
9) Set up iPhone and everything worked perfectly.
10) Wiped laptop (again) and set it up fresh on Big Sur. Everything worked perfectly.
11) Pounded on my chest and declared "I AM ALL THAT IS MAN!" before my girlfriend told me to shut up and go to bed
Here's the kicker--it didn't erase anything. I have all of my messages, all of my passwords, and everything is completely intact. I expected it to be erased entirely and, quite frankly, I was OK with that outcome. So far, everything has been working as it should be (and was).
Happy hunting--hopefully this helps someone else out.