I seemed to have bricked (or pseudo-bricked) my 9160-DK.
In the process of trying to set an APN for my carrier, I seemed to have gotten the modem into a state where it is refusing to respond to most commands.
The Kconfig settings I was trying before this happened were:
CONFIG_PDN=y
CONFIG_PDN_DEFAULTS_OVERRIDE=y
CONFIG_PDN_DEFAULT_APN="hologram"