Leaving 12th night and coming back 20th morning?

Distance from Hampi to Bangalore - 350 kilometres (6 hours)
Distance from Mumbai to Bangalore - 987 kilometres (24 hours)

Distance from Mumbai to Hubli - 593 kilometres (15 hours)
Distance from Hampi to Hubli - 161 Kilometres (2-3 hours)

Distance from Mumbai to Hospet- 840 Kms (30 hours)
Distance from Hospet to Hampi- 30 mins

We will be in Hampi in 20 hours max So if we leave on the
Route Train Bus
1 Mumbai to Bangalore 359 1500, 1000, 700
2 Mumbai to Hubli 259 1000, 950, 700
3 Hubli to Hampi -
4 Bangalore to Hampi
5 Mumbai to Hospet 303(SL)
822(3A) -

Issue with Mumbai to Hospet train, leaves Mumbai at 1 10 am. :(
No other trains to Hospet.

So technically the best option is Mumbai-Hubli-Hampi.

Now, check this out -> http://wikitravel.org/en/Hampi

Distance from Hampi to Coorg- 458 kms (approx 9 hours)

Options: Via train, go from Hampi to Hubli, take a train from Hubli to Mysore. Trains below. Journey from Mysore to Coorg is about 2 and a half hours. Via bus.

Following is the list of all the trains running between Hubli to Mysore Railway Stations:

Train Train Name Origin Departure Destination Arrival M T W T F S S
11035 Sharavathi Express Hubli Jn 12:55 Mysore Jn 21:45 N N Y N N N N
12782 Swarna Jayanthi Hubli Jn 20:20 Mysore Jn 05:05 N Y N N N N N
16209 Ajmer Mysore Express Hubli Jn 17:40 Mysore Jn 07:10 Y N N N N Y N
17302 Dharwar Mysore Express Hubli Jn