Perhaps the chair of the ref's department has your reference's contact info in the remote location.
In this case I think I have more information about his/her whereabouts than they.
Or do you have the reference's cell phone number?
I have one number. I was talking to him/her in the beginning of this month (s/he was already away). Then s/he told me s/he was leaving soon and that was it. I hope s/he checks e-mail at least once a week, but who knows...
In your case it sounds like they prefer to speak to the reference directly, but they might be willing to accept a letter.
No, I think they only want the letter. Too bad they did not ask by e-mail...