AH HA! You have my favorite cocktail of solvents there. Hoppe's #9, Tri-Flow oil, and alcohol. Whoo Hooo!
OK, seriously once clean I lightly, emphasis on lightly, oil any metal to metal parts. The drive gear would get Tri-Flow grease since it's easier to get than the Singer grease.
This would be a good place to try that new Singer style grease sold by Nova Montgomery.
Joe