We report a methodology for measuring 85Kr/Kr isotopic abundances using Atom Trap Trace Analysis (ATTA) that increases sample measurement throughput by over an order of magnitude to 6 samples per 24 hours. The noble gas isotope 85Kr (half-life = 10.7 yr) is a useful tracer for young groundwater in the age range of 5-50 years. ATTA, an efficient and selective laser-based atom counting method, has recently been applied to 85Kr/Kr isotopic abundance measurements, requiring 5-10 microliters of krypton gas at STP extracted from 50-100 L of water. Previously a single such measurement required 48 hours. Our new method demonstrates that we can measure 85Kr/Kr ratios with 3-5% relative uncertainty every 4 hours, on average, with the same sample requirements.