The only fem form of George that I like is Georgina. Georgia is doubly geographical, and some people can't pronounce Georgiana, which is in any case far too long and rhythmically unpleasing.Gen as a nn for Genevieve is pretty standard. So is Genny.
Georgia isn’t a bad name for a girl, but I don’t know if it would be first pick; I kind of like the Jorja spelling! I don’t care for Georgie as a name in general, Genevieve is a very beautiful name, and Gen is a wonderful nickname for Genevieve!