Large-mode-area Yb-doped fiber amplifiers operating at high powers are of interest in many areas of manufacturing, processing, and defense as they bypass the catastrophic power density limits of single-mode fiber devices. As power is increased, thermal mode instability limits the beam quality of these devices due to thermally induced, long-period gratings that couple light out of the fundamental mode. In this work, three fiber designs for delaying the onset threshold of thermal mode instability are investigated using a spatio-temporally resolved model based on that developed by Shadi Naderi, modified for additional physics of temperature dependent modes and our design criteria. The model includes amplifier gain, temperature dependent mode shapes and effective indexes, cross- and self-phase modulation terms, and spatially-dependent coupling between fiber modes based on thermals determined by deposition and diffusion. The three designs include a trefoil multi-core design, a clad linear index-graded design, and a confined gain design. The three independent designs result in over 27%, 50%, and 100% improvement in threshold, respectively. All designs were approached based on the objective to reduce the overlaps between the fundamental mode and the higher-order modes, as well as reduce the higher-order mode overlaps with the gain dopant and thus the area of greatest thermal deposition. All three fibers are designed to have a fundamental mode of similar spatial extent to that of the fundamental mode a of a 50 micron core optical fiber with 0.06NA.