I did try that. Additionally, I have the cellular modem control buttons addon to the powerkey menu, toggling that doesn't seem to affect things either.
Does anyone know how the control button works under the hood? I think it may somehow conflict with offline mode. Have tried toggling both options in various sequences and that doesn't seem to make any difference, but if there was a lower-level way to get at it, I'm quite happy to give that a shot.
As a last resort I could re-flash, but as this is my primary phone I'd rather keep it up and running for as long as possible.