Recently, high-entropy alloys (HEAs) have emerged as a unique platform for discovering superconducting materials and offer avenues to explore exotic superconductivity. The highly disordered nature of HEAs suggests the regular phonon required for BCS superconductivity may be unlikely to occur. Therefore, understanding the microscopic properties of these superconducting HEAs is important. We report a detailed characterization of the superconducting properties of the noncentrosymmetric (α-Mn structure) HEAs (HfNb) 0.10 (MoReRu) 0.90 and (ZrNb) 0.10 (MoReRu) 0.90 by using magnetization, specific heat, AC transport, and muon-spin relaxation/rotation (μSR). Despite the disordered nature, low-temperature specific heat and transverse-field muon spin rotation measurements suggest a nodeless isotropic superconducting gap, and zero-field μSR measurements confirm that time reversal symmetry is preserved in the superconducting ground state.