Current 3D mesh steganography algorithms relying on geometric modification are prone to detection by steganalyzers. In traditional steganography, adaptive steganography has proven to be an efficient means of enhancing steganography security. Taking inspiration from this, we propose a highly adaptive embedding algorithm, guided by the principle of minimizing a carefully crafted distortion through efficient steganography codes. Specifically, we tailor a payload-limited embedding optimization problem for 3D settings and devise a feature-preserving distortion (FPD) to measure the impact of message embedding. The distortion takes on an additive form and is defined as a weighted difference of the effective steganalytic subfeatures utilized by the current 3D steganalyzers. With practicality in mind, we refine the distortion to enhance robustness and computational efficiency. By minimizing the FPD, our algorithm can preserve mesh features to a considerable extent, including steganalytic and geometric features, while achieving a high embedding capacity. During the practical embedding phase, we employ the Q-layered syndrome trellis code (STC). However, calculating the bit modification probability (BMP) for each layer of the Q-layered STC, given the variation of Q, can be cumbersome. To address this issue, we design a universal and automatic approach for the BMP calculation. The experimental results demonstrate that our algorithm achieves state-of-the-art performance in countering 3D steganalysis.