This study addresses the critical technical need to enhance the 1–10 day prediction accuracy of polar motion (PM) in satellite autonomous navigation and deep space exploration, with a focus on optimizing the convolution input accuracy within the least squares and autoregression with effective angular momentum (LS+AR+EAM) method. Through theoretical derivation and numerical experiments, we identify the significant impact of the iterative mechanism of the convolution input in the Liouville equation on PM prediction accuracy. On one hand, it clearly states that the initial step of convolution iteration should begin today using today's daily data, rather than relying on the iterative convolution result from the previous step. On the other hand, due to the requirement for the previous PM, previous geodetic angular momentum (GAM), and current GAM in convolution input, several GAM predictions are constructed using IGS ultra-rapid 6 hr resolution data. Additionally, a hybrid method is used to obtain multiple EAM predictions. By integrating these predictions, the range of prediction errors is effectively constrained. The hindcast results, submitted before 20:00 UTC every Wednesday during the official interval of the second Earth Orientation Parameters Prediction Comparison Campaign (2nd EOP PCC), show that the proposed method improved the mean absolute error (MAE) over the first seven days compared to the first-place method (ID136), with improvements of 51.9%, 32.0%, 28.5%, 20.9%, 19.2%, 17.2%, and 17.0% in the X direction, and 20.6%, 16.2%, 14.4%, 12.8%, 8.7%, 3.1%, and 3.0% in the Y direction. Furthermore, extending the statistical range from 2016/1/6 to 2022/12/28, the proposed method yields MAE values of (0.165, 0.137), (0.735, 0.505), and (1.874, 1.238) mas for days 1, 5, and 10, respectively, outperforming the official predictions by IERS or USNO, which are (0.255, 0.194), (1.534, 1.110), and (2.875, 1.877) mas. This not only validates the stability of the proposed method but also demonstrates its direct applicability in real-world engineering applications.