We report experimental progress toward demonstrating background-limited arrays of membrane-isolated transition-edge sensors (TESs) for the Background Limited Infrared/Sub-mm Spectrograph (BLISS). BLISS is a space-borne instrument with grating spectrometers for wavelengths λ= 35-435 μm and with R= λ/Δλ~500. The goals for BLISS TESs are: noise equivalent power (NEP) = 5×10-20 W/Hz1/2 and response time τ<30ms. We expect background-limited performance from bilayers TESs with TC=65mK and G=15fW/K. However, such TESs cannot be operated at 50mK unless stray power on the devices, or dark power PD, is less than 200aW. We describe criteria for measuring PD that requires accurate knowledge of TC. Ultimately, we fabricated superconducting thermistors from Ir (TC≥135mK) and Mo/Cu proximitized bilayers, where TC is the thermistor transition temperature. We measured the Ir TES arrays in our 45mK base temperature adiabatic demagnetization refrigerator test system, which can measure up to eight 1x32 arrays simultaneously using a time-division multiplexer, as well as our single-pixel test system which can measure down to 15mK. In our previous Ir array measurements our best reported performance was NEP=2.5×10-19 W/Hz1/2 and τ~5ms for straight-beam TESs. In fact, we expected NEP 1.5×10-19W/Hz1/2 for meander beam TESs, but did not achieve this previously due to 1/f noise. Here, we detail improvements toward measuring the expected NEP and demonstrate NEP=(1.3±0.2)×10-19W/Hz1/2 in our single-pixel test system and NEP=(1.6±0.3)×10-19W/Hz1/2 in our array test system.