Why do US SIM cards slow down my Galaxy Note 3, and prevent system settings from opening?
I believe part of the problem is twofold:


All the US phone providers I tried required manual APN configuration. (I've occasionally had to do this for providers in other countries, too.) Of course, configuring this required access to the settings menu. (I would probably have been able to configure this in safe mode, which allowed me access to the settings menu, if this had occurred to me.)
I have Avast Anti-Theft installed, which includes a feature that denies access to the settings menu, when the SIM card changes. Normally, when I change the SIM card, this doesn't inhibit network access (see #1 above), so other security features, such as the email I receive, makes it clearer that Avast Anti-Theft has kicked in, no matter how much of a doofus jetlag makes me.  I suppose this also highlights a workaround for Avast Anti-Theft. Whoopsie! 


I'm pretty sure this is the reason. Unfortunately, I ended up humouring AT&amp;T's opinion that my phone had malware, that somehow only kicked in when I'm in the US, so I wiped my phone, and thus don't know for sure. (I wonder if technical staff in other parts of the world would think malware might attack only their country!)