Robot-assisted Single Port (SP) surgical systems have become popular in laparoscopy, consisting of multiple flexible instruments and an endoscope emerging through a single cannula. This innovative approach presents several challenges related to a smaller workspace and visual field of view. Previous works on Dual-Arm Concentric Tube Continuum Robots (DACTCR) aimed to enhance SP systems by increasing autonomy in a specific surgical subtask, thus simplifying procedures and reducing the surgeon’s workload. This paper extends beyond state-of-the-art methods, particularly the utilization of the relative Jacobian and null-space projection for cooperation control. The main contributions of this paper in simulation involve the incorporation of an actuation limit avoidance solution as an additional block to the DACTCR control system and the evaluation of different promising redundancy resolution techniques like saturation in the null-space and null-space projection, both formulated as constrained quadratic programming problems.