Surgical suturing is a high-precision task that impacts patient healing and scarring. Suturing skill varies widely between surgeons, highlighting the need for robot assistance. Previous robot suturing works, such as STITCH 1.0 [1], struggle to fully close wounds due to inaccurate needle tracking and poor thread management. To address these challenges, we present STITCH 2.0, an elevated augmented dexterity pipeline with seven improvements including: improved EKF needle pose estimation, new thread untangling methods, and an automated 3D suture alignment algorithm. Experimental results over 15 trials find that STITCH 2.0 on average achieves 74.4% wound closure with 4.87 sutures per trial, representing 66% more sutures in 38% less time compared to the previous baseline. When two human interventions are allowed, STITCH 2.0 averages six sutures with 100% wound closure rate. Project website: https://stitch-2.github.io/