Context. Sagittarius A* (Sgr A*) exhibits frequent flaring activity across the electromagnetic spectrum. Signatures of an orbiting hot spot have been identified in the polarized millimeter wavelength light curves observed with ALMA in 2017 immediately after an X-ray flare. The nature of these hot spots remains uncertain. Aims. We expanded existing theoretical hot-spot models created to describe the Sgr A* polarized emission at millimeter wavelengths. We sampled the posterior space, identifying best-fitting parameters and characterizing uncertainties. Methods. Using the numerical radiative transfer code ipole, we defined a semi-analytical model describing a ball of plasma orbiting Sgr A*, threaded with a magnetic field and emitting synchrotron radiation. We then explored the posterior space in the Bayesian framework of dynesty. We fit the static background emission separately, using a radiatively inefficient accretion flow model. Results. We considered eight models with a varying level of complexity, distinguished by choices regarding dynamically important cooling, non-Keplerian motion, and magnetic field polarity. All models converge to realizations that fit the data, but one model without cooling, non-Keplerian motion, and magnetic field pointing toward us improved the fit significantly and also matched the observed circular polarization. Conclusions. Our models represent observational data well and allow testing various effects in a systematic manner. From our analysis, we have inferred an inclination of similar to 155 - 160 deg, which corroborates previous estimates, a preferred period of similar to 90 min, and an orbital radius of 9 - 12.0 gravitational radii. Our non-Keplerian models indicate a preference for an orbital velocity of 0.6-0.9 times the Keplerian value. Last, all our models agree on a high dimensionless spin value (a* > 0.8), but the impact of spin on the corresponding light curves is subdominant with respect to other parameters.