Thank you for working with me on this. Both commands give the same output:
# gsmctl -A 'AT+CGREG?'
+CGREG: 2,1,"4F00","1369022",7
# gsmctl -A 'AT+CEREG?'
+CEREG: 2,1,"4F00","1369022",7
So it seems the info is available via a different register.
Let me know if remote CLI access is still needed and I will make the arrangement.