Well, I took it into the Samsung Customer Service Center and after a little convincing, they looked a little deeper into the battery drain and called me to pick up the phone about 5 hours later.
They replaced the motherboard as well as the charging port and connected sub-board (?).
I was warned off using non-genuine Samsung or 3rd-party cables and chargers, citing that this occurence had been recorded in their database and that a repeat incident could void my warranty. (They said that they know if 3rd-party cables and chargers have been used.)
They didn't replace the battery.
That said, my phone is back to a good "normal" as far as charging speed and charge retention is concerned.
My biggest challenge since picking up my phone is finding a Samsung car charger, as the only current model is sold out in most places. I ended up picking up an OtterBox car charger, as if I can't trust them to stick to quality standards, who can I?
I'm mourning the loss of convenience of my magnetic cables, but it's not worth risking an abnormally-draining phone battery (and not having warranty coverage to get it fixed.)