Given everyone already has domain accounts. Try IIS integrated authentication. You will get an ugly logon box off network but your creds should pass down to the file share.
@lomaxx
Are you saying that only you have perms to the share or that you manually mapped it to a drive letter. If the later you can use ucn \host\share the same way you would use a c:\shared_folder.
Random
Would it be a burden to mirror the share to a local folder on the host? I hear ROBOCOPY is pretty handy.
Another Idea. Run IIS on your target share you can read via http and if you need to write investigate webdav.