JFK-DXB-MUC-DXB-SIN

That's an odd itinerary. OP, is there a particular reasons why you are going to Munich? If not, I can't see the need for this route. It should be possible to fly JFK-DXB-SIN, surely?

I have no experience of long periods between flights at MUC, but I was able to check a bag right through AKL-SIN-LHR, with 11.5 hours on the ground in Singapore. At that time, I understood that this could be done when the interval between flights was less than 12 hours.