Good news from the traditional Benedictine Abbey of Le Barroux in France: it is now possible to follow (part of) the Divine Office sung by the monks according to the Extraordinary Form live via internet at this address: http://www.barroux.org/fr/liturgie/ecoutez-nos-offices.html
The Offices broadcast each day are:
Prime at 7:45 or 8:00 AM CET (= 1:45 or 2:00 AM EST),
Sext at 12:15 PM CET (= 6:15 AM EST),
Vespers at 5:30 PM CET (=11:30 AM EST),
and Compline at 7:45 PM CET (=1:45 EST).
Thanks to a reader for the tip!