Modern AI inference faces an irreducible tension: no single computational resource simultaneously maximizes performance, preserves privacy, minimizes cost, and maintains trust. Existing orchestration frameworks optimize single dimensions (Kubernetes prioritizes latency, federated learning preserves privacy, edge computing reduces network distance), creating solutions that struggle under real-world heterogeneity. We present IslandRun, a multi-objective orchestration system that treats computational resources as autonomous "islands" spanning personal devices, private edge servers, and public cloud. Our key insights: (1) request-level heterogeneity demands policy-constrained multi-objective optimization, (2) data locality enables routing compute to data rather than data to compute, and (3) typed placeholder sanitization preserves context semantics across trust boundaries. IslandRun introduces agent-based routing, tiered island groups with differential trust, and reversible anonymization. This establishes a new paradigm for privacy-aware, decentralized inference orchestration across heterogeneous personal computing ecosystems.