I can set up the environment in a DOS box, but I like to be able to
invoke Vim by using the "edit with vim" context menu item.
Well, if you're comfortable digging around in the registry, you
might be able to find the "edit with vim" key...you might try
HKCR\applications\gvim.exe\shell\edit\command
HKLM\SOFTWARE\Classes\Applications\gvim.exe\shell\edit\command
and change it so that it's something like
...\gvim.exe -u c:\path\to\local\vimrc "%1"
I don't know which bits use those two registry keys (namely, if
the "Edit With Vim" menu option executes the contents of either
of these two keys), but it's worth a stab...
HTH,
-tim