The Laser Interferometer Space Antenna (LISA) will detect gravitational waves (GWs) from dozens of extreme- and intermediate-mass-ratio inspirals (EMRIs/IMRIs). These sources will stay in-band for months to years, offering extraordinary scientific potential. However, their fully phase-coherent analysis standard in current pipelines imposes stringent waveform accuracy requirements; failing to model the signal over such long durations can result in significant systematic biases. To address this, we formulate a robust Bayesian inference framework that segments the data into blocks, infers each block coherently, and recombines the results using loosely-coherent phase information. By restricting full phase-tracking to much shorter block durations, this approach prevents significant accumulation of phase errors. We implement this methodology in (Segmented Posteriors for Long-Inspiral Templates), a GPU-accelerated Python package. Applying to an environment-rich injection, we demonstrate that while a fully-coherent vacuum-GR analysis incurs a maximum 1D systematic bias of $\approx 4.8\sigma$ from the truth, the shorter integration window of our loosely-coherent approach restricts such biases to $\lesssim 0.5\sigma$. Overall, despite a fractional loss of optimal signal-to-noise ratio, the substantial improvement in parameter accuracy offered by our method presents a highly advantageous trade-off for LISA and other future GW detectors.