The above doesn't work with your dates, as AM only fly to NRT on Mondays and Thursdays. Therefore you have to go via LAX on the return.

So
NYC (DL/AM) MEX
MEX-EZE-MEX separate ticket
MEX (AM) LAX
LAX (KE) NRT
NRT (NW) SIN
SIN (CZ) CAN
CAN (CZ) DEL
DEL - BOM "overland" (i.e. buy an oneway domestic ticket)
BOM (AF) CDG
CDG (AF) NYC

Can anyone check whether this is possible on the dates the OP wants it?