#3 can be modified to:
Samalkot/Pitapuram-Kakinada-Kotiapalli-Narasapuram-Machilipatnam
Is a 30KM indirection okay for railways? Then:
Nidadavolu-BVRM JN-Narasapuram-Machilipatnam.
Railways is unlikely to connect BVRM to Mas without connecting Narasapuram.