We present dynamical modeling of the broad-line region (BLR) for the highly variable AGN SDSS J141041.25+531849.0 (z = 0.359) using photometric and spectroscopic monitoring data from the Sloan Digital Sky Survey Reverberation Mapping project and the SDSS-V Black Hole Mapper program, spanning from early 2013 to early 2023. We model the geometry and kinematics of the BLR in the Hβ, Hα, and Mg ii emission lines for three different time periods to measure the potential change of structure within the BLR across time and line species. We consistently find a moderately edge-on (i_{full−state} = 53.29◦ +7.29 −6.55) thick-disk (θ_{opn, full−state} = 54.86◦ +5.83 −4.74) geometry for all BLRs, with a joint estimate for the mass of the supermassive black hole (SMBH) for each of three time periods, yielding log10(MBH/M⊙) = 7.66+0.12 −0.13 when using the full dataset. The inferred individual virial factor f ∼ 1 is significantly smaller than the average factor for a local sample of dynamically modeled AGNs. There is strong evidence for non-virial motion, with over 80% of clouds on inflowing/outflowing orbits. We analyze the change in model parameters across emission lines, finding the radii of BLRs for the emission lines are consistent with the following relative sizes R_{Hβ} ≲ R_{MgII} ≲ R_{Hα}. Comparing results across time, we find R_{low−state} ≲ R_{high−state}, with the change in BLR size for Hβ being more significant than for the other two lines. The data also reveal complex, time-evolving, and potentially transient dynamics of the BLR gas over decade-long timescales, encouraging for future dynamical modeling of fine-scale BLR kinematics.
