A method for controlling handover of a user equipment device (UE) between (i) a first cell site that provides dual-connectivity service on a first radio access technology (RAT) and a second RAT and (ii) a second cell site that provides standalone first-RAT service, wherein the handover includes transitioning the UE from source first-RAT service to target first-RAT service. The method includes setting a handover threshold to use as a basis to evaluate whether target first-RAT coverage detected by the UE is sufficiently stronger than source first-RAT coverage detected by the UE, where setting the handover threshold includes setting the handover threshold to a value selected based on whether the UE has detected that second-RAT coverage of the first cell site meets a defined threshold measurement threshold. Further, the method includes applying the set handover threshold as a basis to control whether to invoke the handover of the UE.