Participatory Design (PD) in Human-Robot Interaction (HRI) typically remains limited to the early phases of development, with subsequent robot behaviours then being hardcoded by engineers or utilised in Wizard-of-Oz (WoZ) systems that rarely achieve autonomy. We present LEADOR (Led-by-Experts Automation and Design Of Robots) an end-to-end PD methodology for domain expert co-design, automation and evaluation of social robots. LEADOR starts with typical PD to co-design the interaction specifications and state and action space of the robot. It then replaces traditional offline programming or WoZ by an in-situ, online teaching phase where the domain expert can live-program or teach the robot how to behave while being embedded in the interaction context. We believe that this live teaching can be best achieved by adding a learning component to a WoZ setup, to capture experts' implicit knowledge, as they intuitively respond to the dynamics of the situation. The robot progressively learns an appropriate, expert-approved policy, ultimately leading to full autonomy, even in sensitive and/or ill-defined environments. However, LEADOR is agnostic to the exact technical approach used to facilitate this learning process. The extensive inclusion of the domain expert(s) in robot design represents established responsible innovation practice, lending credibility to the system both during the teaching phase and when operating autonomously. The combination of this expert inclusion with the focus on in-situ development also means LEADOR supports a mutual shaping approach to social robotics. We draw on two previously published, foundational works from which this (generalisable) methodology has been derived in order to demonstrate the feasibility and worth of this approach, provide concrete examples in its application and identify limitations and opportunities when applying this framework in new environments.