In laser science and industry, considerable effort is directed toward designing fibers for fiber laser and fiber amplifier applications, each of which offers a particular advantage over the others. Evanescently coupled multicore fibers, however, have been studied less extensively due to the relatively small mode area in the single-mode regime. Here, by proposing a new structure with stress-applying parts in a 37-core fiber and optimizing this structure through a comprehensive framework, we present 21 solutions characterized by large-mode-area and high beam quality in the single-mode, single-polarization regime. Different fiber designs are optimal for different output parameters. In one design, the mode area can significantly increase to above 880 μm2, which is comparable with that of photonic-crystal fibers. Moreover, besides the single-mode operation, the beam quality factor (M2 factor) of the fundamental mode is considered an output parameter in the bent state and is improved up to 1.05 in another design. A comprehensive tolerance analysis is then performed to assess the performance of the designs under deviations from normal conditions. Moreover, in spite of the shifts in the loss of modes, the proposed high beam quality LMA fibers maintain single-polarization, single-mode operation across a wide range of core pitches, bending orientation angles, and bending radius deviations. Our results highlight the potential of multicore fibers for the efficient operation of fiber lasers and amplifiers.