Observations of O-bearing molecular ions are frequently used to constrain the physical conditions in the interstellar medium, specifically the H2 fraction, relative to the total hydrogen nuclei number density, and the cosmic-ray ionization rate of atomic H. OH+ traces diffuse clouds with H2 fractions ~0.1. OH+ formation is linked to the cosmic-ray ionization rate of atomic H, which then undergoes charge transfer with atomic O. The resulting O+ can undergo hydrogen abstraction with H2 to form OH+. Hydrogen abstraction can also destroy the resulting OH+. The basic chemical model is completed by dissociative recombination (DR) with free electrons, a competing destruction pathway. A steady-state analysis of this system allows one to estimate the cosmic-ray ionization rates from the observed OH+ abundances. But such models require reliable rate coefficients that account for the internal excitation of the reactants. At the Cryogenic Storage Ring (CSR) in Heidelberg, Germany, we achieve this by storing fast beams of the target ion in a cryogenic environment, where the ions can radiatively relax to their ground vibrational and rotational states. Here, we present merged beams experiments for OH+ interacting with the recently installed electron cooler that enables low energy (meV) electron-ion collision studies, corresponding to a translational temperature ~ 10 K. At these energies, the electrons can not only neutralize OH+ via DR but can also rotationally excite and de-excite the molecules. We took special care in the present experiments to prepare the stored ion beam with a well characterized rotational population when recording DR spectra as a function of center-of-mass collision energy. As we were unable to directly probe the OH+ rotational populations, we devised an experimental scheme that limits the effects of electron collisions on the rotational population evolution versus storage time. Using this scheme, we recorded DR spectra as a function of storage time to generate state-specific DR cross sections. Here, we will present our preliminary results. This project is supported, in part, by the NASA Astrophysics Research and Analysis program under grant 80NSSC19K0969 and by the Max Planck Society.