Alright, I'm back with more testing. I loaded back into my affected save file to move a different sim out via "Split From Household And Move" and in both the recovered save and the original one there was no issue, save for one strange glitch where the available households wouldn't show up one time.
After doing that successfully with a different sim, moving OUT of a household with a sim with an active career, I attempted to move the original sim I was having issues with INTO the household with the active career sim. This did not work, gave me the same error message I originally got, and produced the same line in the Last Exception file, which was:
Attribute Error: "NoneType" object has no attribute "add_knows_career"
This appears to be what the game is flagging as the glitch, and since both times it has happened with active career sims only in these saves, I can only assume the active careers are the issue here. The ongoing problem I am having comprehending this is that it is NOT happening in other save files. I also could not replicate the glitch where the "split from household and move" UI became unusable, as I only used this with the sim moving out and not in.
I strongly encourage anyone on PC/Mac to create a google drive or dropbox folder with both your affected saves and your last exception files in it, and contact @TheSimsDirect to send the sims team these saves to help solve this faster. Make sure the files are EDITABLE so that the sims team can download them to investigate the issue further. And for everyone like me, who can't play their main household because of this, please be patient. This is clearly an elusive glitch affecting multiple packs, on both PC/Mac and console. Sending the sims team your save files is the best way to make the wait time for a fix shorter.