Two-dimensional (2D) materials and van der Waals (vdW) heterostructures provide an exceptional platform for engineering quantum devices, yet realizing their potential requires electrical integration without compromising the pristine properties of atomically thin crystals through conventional nanofabrication. Transferable circuitry addresses this challenge by decoupling circuit fabrication from device assembly, enabling electrical contacting without directly processing the active material. Here, we introduce SiNₓ nanomembrane (NMB) circuits realized through a simplified top-down strategy that reduces fabrication complexity, processing steps and specialized tools required by our previous bottom-up approach. As a stringent benchmark of material preservation, we electrically integrate a four-unit-cell-thick, optimally doped Bi₂Sr₂₋ₓLaₓCuO_(6+δ) (Bi2201) flake and observe a superconducting transition at T_cⁱⁿᶠ~32K, close to the T_cᵒⁿˢᵉᵗ~34K measured by susceptibility in the parent crystals. The preservation of superconductivity demonstrates electrical integration of fragile layered materials without direct exposure to conventional cleanroom procedures, providing a versatile platform for integrating increasingly complicated vdW heterostructures, moiré materials, and hybrid quantum architectures.