Go for Amarkantak.
Only train with GNWL for Itarsi Bilaspur.
Source is Bhopal only, nearby Itarsi. So even reservations would be easier and you won't be at the mercy of trains coming from New Delhi or Indore or Rajasthan.
5 AM arrival is early enough that even if this train gets delayed you'd still have enough time in hand to finish up your work...
more... and move on to Tata Nagar.
It's daily so no issues regarding planning for a specific day of journey.
Although if you're not able to find tickets and you're going on Tuesday then I'd suggest go for Indore Puri Humsafar, almost nearby timings and since it's occupancy is very well known ЁЯШВ, more chance of WL clearing and confirmed seat.