The Electron-Ion Collider (EIC), to be constructed at Brookhaven National Laboratory, will collide polarized, high-energy electron beams with hadron beams, achieving peak luminosities of up to $1.0\times {10}^{34}$ cm${}^{-2}$s${}^{-1}$. To reach such high luminosity, the EIC will employ flat-beam collisions at the interaction point. The design transverse emittance ratio will be about 10:1 in the Hadron Storage Ring (HSR). Thanks to stochastic cooling and precise decoupling, we successfully generated and accelerated gold ion beams with a large emittance ratio of 11:1 in the Relativistic Heavy Ion Collider (RHIC). In this article, we present results of intrabeam scattering (IBS) measurements and modeling for large-emittance-ratio gold ion beams, both without and with controlled betatron coupling. To model the IBS growth, we use the formulas developed by Lebedev and Nagaitsev.