You can take either of the approaches that you're suggesting. The simpler solution would be to grow plants adapted to shade and wet soil. Hostas and sedges would adapt well to this situation, and come in a variety of sizes, textures and colors. You could also create a raised bed or berm of soil to lift the root zones of plants in those areas out of the constantly wet soil. The deeper the raised bed or berm the better, but a minimum of 6 to 12 inches in depth is needed to keep the roots out of the excessively wet zone.