I'm confused about the goal here ---- are you planning a MR for your parents?
Given that there are no direct flights from FRA to LWO, and that SQ's service back to JFK leaves FRA early in the morning, I suspect that your concern about needing to collect luggage in FRA is, at least in part, misplaced --- I don't see how they could connect to this flight without an overnight in FRA.
If the primary goal is to have them travel comfortably to LWO on a * Alliance carrier without enroute stopovers, I'd recommend TK (via IST) or OS (via VIE).... and save the SQ 380 experience for another trip. If the goal is really a MR, please post more details.