jb_miraval Try moving the broken household to a different lot, either a default Maxis house or a blank lot, and see whether you can load them. If not, split them into individual sim households and try again, the idea being that maybe you can isolate the issue to one sim.
Separately, if you're comfortable with various kinds of cheats, you could load a different household and try changing the careers of the sims in your broken household via cheats. I'd have to look up what exact cheats to use and am not sure whether you'd need TwistedMexi's AllCheats, but if you don't know already, I can figure it out for you.
I know you believe they're all in EA careers, but the one LE you posted points to some issue with a career, so one of theirs could be broken anyway. Or maybe you have multiple issues and adding back the custom careers fixed only one of them.
Feel free to post a new LE if you get one.