We study the non-equilibrium structural dynamics of the incommensurate and nearly-commensurate charge-density wave phases in 1T-TaS$_2$. Employing ultrafast low-energy electron diffraction (ULEED) with 1 ps temporal resolution, we investigate the ultrafast quench and recovery of the CDW-coupled periodic lattice distortion. Sequential structural relaxation processes are observed by tracking the intensities of main lattice as well as satellite diffraction peaks as well as the diffuse scattering background. Comparing distinct groups of diffraction peaks, we disentangle the ultrafast quench of the PLD amplitude from phonon-related reductions of the diffraction intensity. Fluence-dependent relaxation cycles reveal a long-lived partial suppression of the order parameter for up to 60 picoseconds, far outlasting the initial amplitude recovery and electron-phonon scattering times. This delayed return to a quasi-thermal level is controlled by lattice thermalization and coincides with the population of zone-center acoustic modes, as evidenced by a structured diffuse background. The long-lived non-equilibrium order parameter suppression suggests hot populations of CDW-coupled lattice modes. Finally, a broadening of the superlattice peaks is observed at high fluences, pointing to a nonlinear generation of phase fluctuations.
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