Kesterite Cu2ZnSn(SxSe1-x)4 (CZTSSe) is an attractive photovoltaic absorber material because of its tunable bandgap, earth abundance, and low toxicity. However, efficiency and open circuit voltage remain significantly below theoretical limits. We recently showed that back-contact engineering with MoO3/Au on exfoliated vapor-deposited kesterite solar cells can improve device performance. Here, we demonstrate more promising results, which translate into high power conversion efficiencies of up to 12.2% for solution-deposited CZTSe with thicknesses as low as 1.1 μm. Time-resolved terahertz spectroscopy of exfoliated films showed significantly faster recombination at the back surface than at the front. When atomic layer deposited Al2O3 was used to passivate the exposed back surface of exfoliated films, front and back surfaces showed nearly identical recombination dynamics. After thermally depositing high work function MoO3 and reflective Au as the back contact on the Al2O3-passivated absorber, we obtained devices with efficiencies of up to 11.6%. Applying the same strategy of exfoliating working devices and engineering the back contact resulted in efficiencies of up to 12.2% for passivation with a 10 nm layer of Se instead of Al2O3. Further development of such passivation and back-contact engineering approaches may lead to higher efficiency devices with absorber thicknesses below 1 μm.