I'd go with AI, because you can check your bags through to KTM. When you arrive at JFK for check-in, provide the agent with your ticket number, and they should be able to print a baggage tag all the way to KTM. You may need to find an experienced agent who knows how to do this, and you should show up early for check-in. You can then pick up your boarding pass at DEL transfer desk.

If you go with SG, you will need to pass through immigration and customs, pick up your baggage, and bring it over to KTM check-in. You will also need an Indian visa for this.