Acoustic and elastic metamaterials have shown potential for many different applications in wave manipulation and structural isolation. Minimization of a scattered wave field has been identified as an important use for such materials, and a wide variety of designs have been proposed for this purpose. Several of these designs face practical challenges (e.g. pentamode designs, which are difficult to manufacture), and many others involve numerous tunable parameters and a large design parameter space (e.g. distributions of resonators), making global search-based optimization less tractable and raising the need for gradient-based methods. In this work, gradient-based optimization governed by partial differential equations (PDEs) is used to optimize acoustic channels in a coiled-space metastructure layer surrounding a rigid acoustic scatterer. The optimization technique is chosen to more feasibly search the design parameter space, and the acoustic channel design is chosen to exploit sound speed optimization as a proxy for channel length optimization to give practically achievable structures. Results are presented for both a single plane wave direction and multiple plane wave directions, as well as for both a single frequency and multiple frequencies. The equivalence of sound speed optimization and channel length optimization is demonstrated for a feasible design minimizing the scattered pressure field. Designs with various numbers of optimized channels are also considered.