I finally figured out the problem. I was running this through WinPython, and its batch files that set the environment prior to running python.exe assign a value to HOME (that is not the current user's home directory). Apparently, that confuses ssh because when I tweaked my process for starting python.exe in WinPython to clear the HOME variable, that fixed the problem.

…so the problem has nothing to do with GitPython, but others attempting to use GitPython under WinPython will likely encounter the same problem.

My specific fix was to stop using WinPython's scripts/python.bat to run Python and to instead call its scripts/env.bat to set up the environment, then SET HOME=, then execute if not "%WINPYWORKDIR%"=="%WINPYWORKDIR1%" cd %WINPYWORKDIR1% followed by "%WINPYDIR%\python.exe" %* as scripts/python.bat would do.