Discovery of causal relations is an important part of data analysis. Recent exact Boolean optimization approaches enable tackling very general search spaces of causal graphs with feedback cycles and latent confounders, simultaneously obtaining high accuracy by optimally combining conflicting independence information in sample data. We propose several domain-specific techniques and integrate them into a core-guided maximum satisfiability solver, thereby speeding up current state of the art in exact search for causal graphs with cycles and latent confounders on simulated and real-world data.