Prehensile object rearrangement in cluttered and confined spaces has broad applications but is also challenging. For instance, rearranging products in a grocery or home shelf means that the robot cannot directly access all objects and has limited free space. This is harder than tabletop rearrangement where objects are easily accessible with top-down grasps, which simplifies robot-object interactions. This work focuses on problems where such interactions are critical for completing tasks and extends state-of-the-art results in rearrangement planning. It proposes a new efficient and complete solver under general constraints for monotone instances, which can be solved by moving each object at most once. The monotone solver reasons about robot-object constraints and uses them to effectively prune the search space. The new monotone solver is integrated with a global planner to solve non-monotone instances with high-quality solutions fast. Furthermore, this work contributes an effective pre-processing tool to speed up arm motion planning for rearrangement in confined spaces. The pre-processing tool provide significant speed-ups (49.1% faster on average) in online query resolution. Comparisons in simulations further demonstrate that the proposed monotone solver, equipped with the pre-processing tool, results in 57.3% faster computation and 3 times higher success rate than alternatives. Similarly, the resulting global planner is computationally more efficient and has a higher success rate given the more powerful monotone solver and the pre-processing tool, while producing high-quality solutions for non-monotone instances (i.e., only 1.3 buffers are needed on average). Videos of demonstrating solutions on a real robotic system and codes can be found at https://github.com/Rui1223/uniform object rearrangement.