two months in india, route suggestion?

Hi here,

I have planned to travel in india from JAN.10 to MAR.20, after a short stay in singapore, . and will fly to Thiruvananthapuram the first step. and then north to delhi, and east to kolkata, from there leave to thailand. after a study on maps, here is what i'm thinking about:

trivandrum airport - Varkala: by taxi
Varkala - kollam
kollam - alleppey (backwater)
alleppey - kochi (by train, might visit munnar before)
kochi - bangalore - hampi (by train, might visit madurai beofre?)
hampi - goa (train available? no clue which areas in goa to go yet)
goa - mumbai (by train)
mumbai - jadhpur (might visit Udaipur in between?)
jadhpur - jaisalmer
jaisalmer - jaipur
jaipur - agra (includ. orchha)
agra-delhi
delhi - amritsar
amritsar - varanasi
varanasi-kolkata

this has includ. most the places recommended. but as Udaipur seems not approachable by train, and amritsar is a bit outside...any comments and suggestions here for the route considering the time and local festivals? and I would like to travel around by train as much as possible when it's convenient...

thanks all!