For the High-Luminosity (HL-LHC) phase, the upgrade of the Compact Muon Solenoid (CMS) experiment at CERN will include a novel MIP Timing Detector (MTD). The central part of MTD, the barrel timing layer (BTL), is designed to provide a measurement of the time of arrival of charged particles with a precision of 30 ps at the beginning of HL-LHC, progressively degrading to 60 ps while operating in an extremely harsh radiation environment for over a decade. In this paper we present a comparative analysis of the time resolution of BTL module prototypes made of LYSO:Ce crystal bars read out by silicon photo-multipliers (SiPMs). The timing performance measured in beam test campaigns is presented for prototypes with different construction and operation parameters, such as different SiPM cell sizes (15, 20, 25 and 30 μm), SiPM manufacturers and crystal bar thicknesses. The evolution of time resolution as a function of the irradiation level has been studied using non-irradiated SiPMs as well as SiPMs exposed up to 2 × 10¹⁴ n_eq/cm² fluence. The key parameters defining the module time resolution such as SiPM characteristics (gain, photon detection efficiency, radiation induced dark count rate) and crystal properties (light output and dimensions) are discussed. These results have informed the final choice of the MTD barrel sensor configuration and offer a unique starting point for the design of future large-area scintillator-based timing detectors in either low or high radiation environments.