End-to-end 5G network slicing that spans across diverse access and core networks, as well as cloud and edge infrastructure, promises to satisfy on-demand the requirements of different vertical applications in a fast and cost-efficient manner. However, in order to achieve this, slice management systems need to combine different types of orchestrators. The combined usage of such orchestrators can be performed in many ways and related studies of standardization bodies have led to various open issues. This paper presents a solution based on a multi-tier orchestrator which glues NFV, MEC, and Cloud-native orchestrators using API abstraction layers and inter-orchestrator coordination workflows, while revisiting some standardized directives for NFV-MEC integration. The multi-tier orchestrator is evaluated against standard approaches that are based on the aforementioned directives, showing performance enhancements of up to 13x in terms of CPU load of certain orchestrator hosts in scenarios where up to 15 services are instantiated concurrently in an integrated NFV-MEC environment.