Since the question has now narrowed down to "who lost the minus sign" in the Christoffel symbol, let me start a new thread: The OP asks for a reputable source, later than Einstein's 1916 paper, in which the minus sign is abandoned. I propose that it was Einstein himself who dropped it. Below I copy from his <A HREF="https://einsteinpapers.press.princeton.edu/vol7-doc/593">1921 lectures</A> at Princeton University, page 46:

<IMG SRC="https://ilorentz.org/beenakker/MO/Einstein_1922.png"/>