Disclosed are methods and systems for configuring service of a user equipment device (UE). When the UE has dual-connectivity service, such as EN-DC service, poor quality on one of the UE's air-interface connections could result in transition of the UE to single-connectivity service. To address technological issues that may arise in this process, one of the UE's serving Node-Bs (NBs) could control teardown of an access bearer homed to the other of the UE's serving NBs. Further or alternatively, a control-plane signaling path that is homed to one of the UE's serving NBs could be replaced with a control-plane signaling path instead homed to the other of the UE's serving NBs. In addition, in appropriate circumstances, when such reconfiguration occurs, service of the UE could be switched from one core network to another.