On SQ SIN-FRA-NYC is the same plane but you have to get off in FRA as the plane is thoroughly serviced. You are also required to be security screened and that at FRA is almost always awful. There's a thread in the LH forum about the deliberately difficult behaviour of security staff at FRA which includes refusing to speak any language except German and while I speak it I can certainly vouch for awful security experiences there over many years. An encounter with FRA security staff can make you think of the very darkest period of German history. Rumour has it that LH are starting to recruit their own staff as they have so much disruption from people missing connecting flights or just missing flights all together because they are held up in security so FRA really is a place to avoid.

LX would be a good alternative, I don't much like the seats - too coffin like for me but ZRH is a good place to connect and the lounges are passable though LX food seems on the way down at the moment. I would seriously consider LO if the price is good and connecting at WAW is easy. LO are under rated.