The current document is directed to an integrated cloud-management facility, or subsystem, that incorporates an automated-application-deployment-facility integrator that incorporates one or more automated-application-deployment facilities into the cloud-management facility. The automated-application-deployment-facility integrator allows users of the cloud-management facility to access one or more automated-application-deployment facilities within the context of the cloud-management facility. The automated-application-deployment-facility integrator provides to system managers and administrators, through the cloud-management facility, a wider range of functionalities and capabilities than is provided by a cloud-management facility that includes only a single automated-application-deployment facility, or subsystem.