Serverless computing has recently been presented as an effective technology for handling short-lived compute tasks in the cloud. It has the potential of becoming an attractive option also in the context of edge computing where resource-aware deployment, constrained by both limited edge computing resources and experienced latency, plays a vital role. In this paper, we present and experimentally validate a framework that oversees serverless applications in an edge computing scenario. It completely automates serverless application deployment and provides hitless dynamic migration of application compute tasks between a pair of edge nodes, paving the way for handling significantly more complex cases. The framework relies on an integrated deployment, monitoring and offloading infrastructure that enhances AWS IoT Greengrass features and performance. Our implementation provides two separate options for relocating compute tasks by steering application traffic towards the most suitable node. One builds on an on-the-fly application component reconfiguration, while the other selects the suitable node through P4 in-network processing of resource metrics emitted by the nodes. Our experimental demonstration evaluates the migration performance using a latency-sensitive application decomposed to serverless functions. Results reveal extremely fast dynamic reconfiguration and traffic rerouting operations. The used methods avoid congestion peaks at the edge and show no end-to-end latency increase upon migration between the nodes.