I still haven't finished my first apocalypse attempt after over a decade(!) - but let's see...
I might have misremembered, I thought there were already some versions of an Apocalypse/BACC Combo, but so far I only found the rulesets by Darthfluffle and Phaneoh:
DarthFluffle's Apocalypse-themed BACC rules
Phaenoh's Apocalypse Challenge - Realistic/Tiered Variant (not really BaCC, but allows lifting restrictions in tandems)
Aside from that: you're right that most BaCC rulesets restrict careers you can take, while the apocalypse restricts stuff you can do unless a career is topped. So I guess, one idea could be, that the rules in the apocalypse that would make it impossible to lift the restrictions imposed by the BaCC on careers be removed or made weaker, like buying community lots (Business), leaving the lot (military), inviting spouses in (hopelessness) or the restriction on Careers by the BaCC's (restrictions for taking military for example, if you fight zombies in an apocalypse etc.)
On the other side, since BaCC's deal from the start or later with multiple households, it sounds reasonable that the obligation to lift careers is distributed among them - unless you want only one or every household to lift all the apocalypse restrictions, but then you're playing one or several apocalypse challenges in a BaCC hood with no real impact on each other....
Another idea could be, that lifting a restriction would require several Sims in that career, thought perhaps not at the top of the career - a general alone can't fight a zombie horde, and an army with everybody being a general doesn't make that much sense either...
Cyjons Job Stopinator might help here...
Hope this helps!
![^^ ^^](./images/smilies/%5E%5E.gif)