Successful social influence, whether at individual or community levels, requires expertise and care in several dimensions of communication: understanding of emotions, beliefs, and values; transparency; and context-aware behavior shaping. Based on our experience in identifying mediation needs in social media and engaging with moderators and users, we developed a set of principles that we believe social influence systems should adhere to to ensure ethical operation, effectiveness, widespread adoption, and trust by users on both sides of the engagement of influence. We demonstrate these principles in D-ESC: Dialogue Assistant for Engaging in Social-Cybermediation, in the context of AI-assisted social media mediation, a newer paradigm of automatic moderation that responds to unique and changing communities while engendering and maintaining trust in users, moderators, and platform-holders. Through this case study, we identify opportunities for our principles to guide future systems towards greater opportunities for positive social change.