The micromechanical valves that are used in microfluidic large-scale integration (mLSI) technology enable automated control of (bio)chemical and cell-based assays as they can perform crucial functions such as metering, mixing, pumping, and compartmentalization. The mLSI requires flow channels with a rounded profile for leak-free valve operation (i.e. ON/OFF flow control) to execute these functions. Here, we have used the deflection of an elastomeric membrane (DEM) in two configurations; free and constrained deflection, to fabricate reusable and tunable multi-height molds that in turn lead to fabrication of valvable flow channels in an unprecedented height range (up to 220 (130) µm for free (constrained) deflection) for mLSI. The constrained deflection configuration enabled the fabrication of channels that are directly in contact with a substrate, which combines the advantages of push-down and push-up valves that are commonly used in mLSI. Compared to the use of rigid master molds, fabricated either by photolithography on silicon wafers or via other processes such as 3D printing, milling etc, the tunability advantage of the multi-height DEM molds, eliminates the requirement of a different mold for each channel height, thus increases the prototyping and device optimization efficiency. We have developed functional devices to demonstrate that our enhanced soft lithography technique is high-throughput, scalable, and reproducible. The flow of large particles (110 µm diameter) were controlled that shows the suitability of the technique for organ- or spheroid-on-a-chip applications. The electrical resistance of liquid metal in microfluidic channels is modulated with a frequency of 1 kHz, showing the potential for re-configurable electronic circuits.