The distance between Devakottai to Rameshwaram is about 110 Km. (give or take 20 km). Since you plan to travel on 30th of this month, I don't hold any hope of you getting any comfy seat in a train. There seem to be no train between 12 noon and 14:00 hrs. Moreover, the train takes about 5 hrs and however you hurry, you can't reach temple within 6 hrs. minimum from Devakottai to the Temple. About same time will be taken by bus.
I reckon you require 4 or 5 hrs to to perform obligatory rites and have darshans at Rameshwaram. I am presently counting Dhanushkoti out of your present sojourn.
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getting into the options available for travel, please permit me let you know what can be done or performed at Rameshwaram within the span of 5 hrs.
* Reach the Main Temple and without entering temple go to bathing ghat. Take off your clothes and put them into your carry bag. Wear another small dhoti and take at least 3 dips at the bathing ghat. Come out and wearing the same wet dhoti you have to get enter the Temple's outer premises for getting bathed in 22 wells. (You can't have Darshan with a wet cloth). As you start your short walk towards the Temple, you will find someone with a bucket and rope offering you 22 well bathing ritual. He might charge Rs. 200/ - ( including Rs. 25/- for the premise ticket which he will pay and take).
Now, where will you keep your luggage? Immediately on coming out of bathing ghat, to your right, you will find Sri Shankara Mutt. Certainly there will be someone from the mutt who would offer you services of getting drenched in 22 wells standing there. Or else you just enter the gate and politely ask and I am sure they will help you with a locker or a room with lock etc. free of cost. You may pay while leaving any donation to the mutt.
After the round of bathing and after taking Koditheertham (Final holy water) for your near and dears, you have to dry yourself and change to dry clothes and again enter the Temple for Darshan.
After Dharshan, please hire an auto (exclusively) and visit all kundams, theerth and temples, a list of which is readily available with those persons. You may take the help of the person who had assisted you in bathing.
There are 9 important places within Rameshwaram and an auto fellow will take you around and leave you in railway station. Prior to coming to railway station, don't forget to take a take away meal in one very good restaurant (Forgot the name).
Better to be at the station at least 20 minutes prior to departure time.
In my opinion, you should be at the bathing point of the sea by 15:30 hrs so that you get 4 hrs and 30 minutes clear.
Therefore, if you are planning to leave Devakottai by 13:00 hrs, the only way you can feel the joy of visiting Rameshwaram is by taking a cab. If you take bus or that 11:30 train, you can rejig the program. That is after Darshan, see if you have time. You require at least 1 hour for hurrying through all 9 places and another 30 minutes for getting your dinner pack, reach station and settle in your seat.
All the best. When He Calls we all Go!!!
C K