Neural architecture search has proven to be highly effective in the design of computationally efficient, task-specific convolutional neural networks across several areas of computer vision. In 2D human pose estimation, however, its application has been limited by high computational demands. Hypothesizing that neural architecture search holds great potential for 2D human pose estimation, we propose a new weight transfer scheme that relaxes function-preserving mutations, enabling us to accelerate neuroevolution in a flexible manner. Our method produces 2D human pose network designs that are more efficient and more accurate than state-of-the-art hand-designed networks. In fact, the generated networks can process images at higher resolutions using less computation than previous networks at lower resolutions, permitting us to push the boundaries of 2D human pose estimation. Our baseline network designed using neuroevolution, which we refer to as EvoPose2D-S, provides comparable accuracy to SimpleBaseline while using 4.9x fewer floating-point operations and 13.5x fewer parameters. Our largest network, EvoPose2D-L, achieves new state-of-the-art accuracy on the Microsoft COCO Keypoints benchmark while using 2.0x fewer operations and 4.3x fewer parameters than its nearest competitor.