ETA Sorry, I see it's ZH. Ignore my previous comment. (Note to self: Call Augenarzt, schedule that cataract op...)
It's not the border authority that matters, rather the cantonal Veterinäramt. BSL is solely a cantonal matter.
If the dog is an AmStaff mix, then the dog is banned in canton ZH, full stop. You may not import, or keep, a dog with 10% or more DNA match with any of the List 2 breeds. But here's the kicker - in practice, phenotyping, at the discretion of the Veterinäramt, is used to determine if a dog is part List 2.
Yes, I know it says mixed breed. But if you have been told there is AmStaff in the mix, in all good conscience you need to act with that in mind. Don't even think about it, the dog risks euthanasia if someone complains.
The time for grandfathering is years past, no List 2 dogs may be brought into the canton.
See this summary of ZH regs, complied by Tier Im Recht Foundation. Links to the actual text of the law are at the top of the page.
https://www.tierimrecht.org/de/recht/hunderecht/zurich/
Sorry the news isn't what any of us want to hear. BSL is bad science, bad law.
ETA2:
One way to help the dogs that cannot be easily homed is to financially support the shelter, perhaps offer a 'Patenschaft' specifically for these dogs. Just a thought.