We report the exclusive photoproduction cross sections for the Sigma(0)(1385), Lambda(1405), and Lambda(1520) in the reactions gamma + p -> K+ + Y* using the CLAS detector for energies from near the respective production thresholds up to a center-of-mass energy W of 2.85 GeV. The differential cross sections are integrated to give the total exclusive cross sections for each hyperon. Comparisons are made to current theoretical models based on the effective-Lagrangian approach and fit to previous data. The accuracy of these models is seen to vary widely. The cross sections for the Lambda(1405) region are strikingly different for the Sigma(+)pi(-), Sigma(0)pi(0), and Sigma(-)pi(+) decay channels, indicating the effect of isospin interference, especially at W values close to the threshold.