I think I took the contact number from this forum only. You can contact
Sundar Sastrigal - 09443321641. He will arrange everything. He is also the Manager/Chief of Kanchi mutt there. So he can book the room and arrange for other logistics.
I took the train from Chennai and reached Rameswaram in the morning, went to Kanchi mutt through an auto.
Morning, we went to Danushkoti through a jeep and did tharpanam there. Then came back to Agni Theertham (Next to the mutt lodge). From there went to the temple to have darshan.
Returned through an evening train.
Did the same again, after visiting Kashi.