You do not specify what's wrong with opening a new GUI emacs window. If the problem is the long startup time you may consider using emacsclient as your editor. In a nutshell you run (server-start)
in your emacs init file and keep your regular GUI emacs open, and then tell git to use an editor called emacsclient. What happens is that the edited file pops up in a new buffer in your running emacs. After you are done with it you press C-x #
to finish the emacsclient session and then git (or other shell process that started the editor) knows that the editor "emacsclient" is done with the file and continues with its thing. ("emacsclient" is also one word, so it solves your immediate problem too)
Even when your editing has to be done in the terminal window you can run emacsclient -nw
and eliminate the long startup time. There are more possibilities, man emacsclient
is a good read.