Myocardial point tracking (MPT) has recently emerged as a promising direction for motion estimation in echocardiography, driven by advances in general-purpose point tracking methods. However, myocardial motion fundamentally differs from motion encountered in natural videos, as it arises from physiologically constrained deformation that is spatially and temporally continuous throughout the cardiac cycle. Consequently, motion trajectories typically remain locally confined despite substantial tissue deformation. Motivated by these properties, we revisit the architectural design for MPT and find that coarse initialization in commonly used two-stage coarse-to-fine architectures may be unnecessary in this domain. In this work, we propose a fine-stage-only architecture, \textbf{EchoTracker2}, which enriches pixel-precise features with local spatiotemporal context and integrates them with long-range joint temporal reasoning for robust tracking. Experimental results across in-distribution, out-of-distribution (OOD), and public synthetic datasets show that our model improves position accuracy by $6.5\%$ and reduces median trajectory error by $12.2\%$ relative to a domain-specific state-of-the-art (SOTA) model. Compared to the best general-purpose point tracking method, the improvements are $2.0\%$ and $5.3\%$, respectively. Moreover, EchoTracker2 shows better agreement with expert-derived global longitudinal strain (GLS) and enhances test-rest reproducibility. Source code will be available at: https://github.com/riponazad/ptecho.