This study investigates the evolution of miscible Rayleigh-Taylor (RT) turbulence following gravity removal or gravity reversal at different stages of development, using high-resolution numerical simulations combined with Lagrangian passive-particle tracking. From an Eulerian perspective, gravity reversal transforms the unstable RT layer into a weakly turbulent, stably stratified flow with a thick mixed region, whereas gravity removal leads to a freely decaying coasting state that preserves the large-scale imprint of the pre-switch RT structures. The evolution of the mixing-layer width, interfacial dynamics, and anisotropy shows that gravity reversal suppresses entrainment, enhances molecular mixing, and induces decaying oscillations governed by the Brunt-Vaisala dynamics of the post-reversal layer. From a Lagrangian perspective, both single-particle and pair dispersion are strongly non-stationary, anisotropic, and history dependent. Under constant gravity, particle transport is super-diffusive and may even become super-ballistic, owing to sustained buoyancy-driven amplification of the velocity field; the measured scaling further depends on the time origin chosen for particle tracking. After gravity modification, transport is markedly altered: gravity reversal suppresses dispersion most effectively by erasing vertical velocity memory, whereas gravity removal preserves inertial memory and sustains stronger post-switch transport. Statistics of trajectory acceleration, curvature, and their joint distributions further reveal that acceleration history modifies not only the intensity of transport but also the geometry of particle trajectories. These results demonstrate that Lagrangian RT turbulence under constant and time-dependent accelerations requires a history-dependent description beyond the standard framework of stationary turbulence.