The current document is directed to an automated-application-release-management subsystem that executes application-release-management pipelines that includes one or more tasks and/or stages, execution of which launch execution of scripts on specified host computers. The capability for launching scripts from application-release-management-pipeline tasks and stages provides flexibility in design and development of application-release-management pipelines and provides an incremental path for migration of legacy-script-based application-release management to automated pipeline-based application-release management.