Shaping multi-megawatt loads, such as data centers, impacts generator dispatch on the electric grid, which in turn affects system CO2 emissions and energy cost. Substantiating the effectiveness of prevalent load shaping strategies, such as those based on grid-level average carbon intensity, locational marginal price, or marginal emissions, is challenging due to the lack of detailed counterfactual data required for accurate attribution. This study uses a series of calibrated granular ERCOT day-ahead direct current optimal power flow (DC-OPF) simulations for counterfactual analysis of a broad set of load shaping strategies on grid CO2 emissions and cost of electricity. In terms of annual grid level CO2 emissions reductions, LMP-based shaping outperforms other common strategies, but can be significantly improved upon. Examining the performance of practicable strategies under different grid conditions motivates a more effective load shaping approach: one that "cherry-picks" a daily strategy based on observable grid signals and historical data. The cherry-picking approach to power load shaping is applicable to any large flexible consumer on the electricity grid, such as data centers, distributed energy resources and Virtual Power Plants (VPPs).