We have to remember the scale of the project I am proposing is not nearly as momentous as Cape to Cairo or even the London Underground.
Referring back to my map in the OP.
1) Connect India Rail to Burma Rail
We're building a railway from the existing Indian line at Chittagong (now Bangladesh) to the existing line at Myingyan, Burma.
This is 236 miles as the crow files, http://www.distancecalculator.net/from-myingyan-to-chittagong so this would likely be a rail connection of 350 miles or so. Yes, the terrain will be nasty, but not impassable, and labour is extremely cheap and plentiful.
It's not impassable, but it's much worse than anything between the Cape and Cairo. The only African railways this mountainous are the ones in the Horn of Africa, in Ethiopia and Eritrea... and those are truly terrible.