We have fabricated and characterized test devices of a new geometry for cryogenic dark matter search superconducting sensors. The modified design uses the same photolithography masks used to fabricate earlier-generation devices, but with the Al and W films deposited in reverse order. This inverted film geometry (Al over W instead of our conventional W over Al) offers a simplified and robust way to dramatically increase the thickness of Al energy-collecting fins coupled to thin W-TESs—tungsten-transition edge sensors. Data are presented from experiments with inverted geometry test devices exposed to X-rays from a NaCl fluorescence source. The results are compared to data obtained with similar devices fabricated in the standard, non-inverted geometry.