You could try a combination of hobocopy and psexec. Something like this:
psexec \remotemachine -u username \path\to\hobocopy \path\to\src \path\to\dest
Which would run hobocopy on the remote machine, where it would be able to make shadow copies. Note that
\path\to\hobocopy are on the remote machine, although you could make the destination path something like
\\localmachine\share\path\to\dest to do a network copy back over to your own machine. Seems like it would be easier just to copy it locally and then go retrieve the file as a separate step.
You'll need to make sure hobocopy is available on the remote machine, too, including installing the C runtime there if necessary.