Accurate modeling of small-scale redshift-space clustering is crucial for full shape RSD analyses, where satellite galaxies contribute to 1-halo terms and Finger-of-God distortions. We investigate halo reconstruction based on the cylinder grouping (CG) method of Okumura et al.~(2017), which selects an effective halo center tracer from the observed galaxy distribution, and how it impacts cosmological parameter inference. Using DESI-like luminous red galaxy mock catalogs from the AbacusSummit simulations at $z=1.1$, we perform effective field theory (EFT)-based full-shape modeling of the power spectrum of the reconstructed-halo sample. We show that the dominant reconstruction-induced systematics can be described and incorporated within the standard EFT framework. In particular, a simple multipole-dependent rescaling inferred directly from the data on large scales captures the dominant effect, while residual small-scale changes are absorbed by the standard counterterm and stochastic sector, without introducing additional reconstruction-specific parameters. The reconstructed-halo sample yields unbiased constraints on cosmological parameters, including the growth rate $f{\sigma }_{s8}$ and Alcock-Paczynski parameters. Compared to the galaxy sample, it enables both improved robustness and increased statistical precision: at the fiducial limit of $k_{\max}=0.2\,h\,{\rm Mpc^{-1}}$, the uncertainty on $f{\sigma }_{s8}$ is reduced by more than $20\%$, while the high-$k_{max}$ diagnostics show comparatively stable goodness of fit and nuisance parameters.