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tokens: We dedicate this paper to the memory of Neil Gehrels, the P.I. of Swift and a leading author of this paper. Neil was a great scientist who also brought out the best in others. He led the Swift team with enthusiasm and expertise, always happy and eager to take the satellite in new directions. For example, his strong and unwavering support is what allowed Swift to gather these unprecedented data on NGC 5548 and NGC 4151, providing a powerful method that should continue to inform our understanding of AGN physics for years to come. Specifically, without his courageous approval of increased UVOT filter changes well beyond the design lifetime of the filter wheel, the extraordinary 11-band light curve in Figure 3 , which forms the basis of this work, could not have been gathered. This is but one tiny piece of the rich legacy that he leaves us. We further thank the entire Swift team for their tireless dedication and flawless execution of these programs and acknowledge the use of public data from the Swift data archive. We also thank the anonymous referee for helpful and timely reports. This research has made use of the XRT Data Analysis Software (XRTDAS) developed under the responsibility of the ASI Science Data Center (ASDC), Italy. R.E. gratefully acknowledges support from NASA under awards NNX13AC26G, NNX13AC63G, and NNX13AE99G. J.M.G. acknowledges support from NASA under award NNH13CH61C. Research by A.J.B. and H.A.V. was supported by NSF grant AST-1412693. K.H. acknowledges support from STFC grant ST/M001296/1. M.B. gratefully acknowledges support from the NSF through CAREER grant AST-1253702. S.M.C. and E.R.C. gratefully acknowledge the receipt of research grants from the National Research Foundation (NRF) of South Africa. P.E. and K.P. acknowledge support from the UK Space Agency. A.V.F. and W.Z. are grateful for financial assistance from NSF grant AST-1211916, the TABASGO Foundation, and the Christopher R. Redlich Fund. D.C.L. gratefully acknowledges support from NSF under grants AST-1009571 and AST-1210311. T.T. has been supported by NSF grant AST-1412315 and by the Packard Foundation in the form of a Packard Research Fellowship. M.V. gratefully acknowledges support from the Danish Council for Independent Research via grant no. DFF 4002-00275.