RTW would be unlikely. The path NYC-EZE is east and SIN-BOM is west. Unless there is a RTW ticket that considers SIN and BOM in the same region so that it is not backtracking that would not work. Also, you'd have to go BOM-NYC westward at the end, which is not possible without putting another stop in the trip.
I was pretty sure that AF had a CDG-SIN flight but that didn't come up in the SkyTeam search and I didn't dig too hard. There is a 12 hour layover in Paris if you want that:
[KVS Availability Tool 3.1.0/Platinum - Amadeus: Timetable/NL-BCDF]
Code:
EZE Buenos Aires Ministro Pistarini BA AR [SAEZ]
SIN Singapore Changi SG [WSSS]
TUE 19 Aug 2008 - 26 Aug 2008
Carrier Flight From Depart To Arrive A/C St Frequency | Dur'n | Dep T | Arr T | Effect | Ending | Exceptions
--------- ------ ---- --------- ---- --------- ---- ---- ----------------------------------------------------------------
AF 415 EZE 17:05 CDG 11:00 +1 772 0 1234567 37:40 - 2E 30 Apr 11 Oct
-> AF 256 CDG 23:15 +1 SIN 17:45 +2 77W 0 2E 1
As for alternate routings from EZE-SIN, there aren't a ton that operate on Fridays, according to KVS, though the initial search I did on KVS didn't include the AF trip, so who knows. The shortest routing seems to be the MH flight EZE-KUL-SIN, but that is only offered once per week, according to KVS, and not on the day the OP needs it. The routing on MH via CPT is only offered 2x weekly, also on the wrong days for the OP. There is a daily flight on SA at 1800 from GRU-JNB, and SQ can connect you on from there, but I think it will not be possible to finist at 1400 in EZE and make the 1800 from GRU.