Although the case for a swift climate transition is clear, its macro-financial viability remains uncertain. To shed light on the macroeconomic and financial response to deep mitigation trajectories controlled by carbon pricing, we soft-link a process-based integrated assessment model (the World Induced Technical Change Hybrid, WITCH) to a macro-financial agent-based model (the Dystopian Schumpeter Meeting Keynes, DSK). The hybrid framework allows us to translate energy systems transformations into macro-financial outcomes at business cycle frequency. We find that rapid transitions induced by fast-growing carbon prices significantly impact unemployment, inflation, and income distribution. Stabilization policies reduce these economic fluctuations, though not completely so in Paris-compatible scenarios. Our paper emphasizes the need for coordinated climate and macroeconomic policy during decarbonization. Additionally, it showcases how model integration can lead to a better understanding of the economic implications of low-carbon futures.