Dear Edwin,
In order to check whether the Lorentz gamma is actually a time transformation, I looked into en.wikipedia.org/wiki/History_of_Lorentz_transformations and found confirmed that not Einstein but Lorentz dealt with Fitzeau and aberration:
"In order to explain the aberration of light and the result of the Fizeau experiment in accordance with Maxwell's equations, Lorentz in 1892 developed a model ("Lorentz ether theory")."
"Similar transformations were introduced ... by Lorentz (1892, 1895) who analyzed Maxwell's equations, they were completed by Larmor (1897, 1900) and Lorentz (1899, 1904), and brought into their modern form by Poincaré (1905) who gave the transformation the name of Lorentz.[13]".
My best regards,
Eckard Blumschein