I called tech support via the ST 800 number. Make sure to call from a different phone than the one having trouble. They talked me through the usual "check this, check that" troubleshooting. They have to do this first, just to make sure I had everything set right on my phone. Then, they said they'd send a new SIM card. I received the card in the mail rather quickly, and called tech support back per the enclosed instructions. They talkedme through installation and activating the new SIM card (wait to install until they tell you to). Everything is working properly as it should again. I once again have full speed LTE and am getting email notifications pushed properly. Hopefully this problem will stay resolved and not come back. If it does, I'll post back here. If not, it's safe to assume that everything is good.