Cables are commonplace in homes, hospitals, and industrial warehouses and are prone to tangling. This paper extends prior work on autonomously untangling long cables by introducing novel uncertainty quantification metrics and actions that interact with the cable to reduce perception uncertainty. We present Sliding and Grasping for Tangle Manipulation 2.0 (SGTM 2.0), a system that autonomously untangles cables approximately 3 meters in length with a bilateral robot using estimates of uncertainty at each step to inform actions. By interactively reducing uncertainty, Sliding and Grasping for Tangle Manipulation 2.0 (SGTM 2.0) reduces the number of state-resetting moves it must take, significantly speeding up run-time. Experiments suggest that SGTM 2.0 can achieve 83% untangling success on cables with 1 or 2 overhand and figure-8 knots, and 70% termination detection success across these configurations, outperforming SGTM 1.0 by 43% in untangling accuracy and 200% in full rollout speed. Supplementary material, visualizations, and videos can be found at sites.google.com/view/sgtm2.