I had never had a problem checking additional bag in FRA with LH 10 hours before my next flight. You are 1P, i.e. *G so just go to the First Class Checkin counter and tell them you want to check additional bag once you have landed.

This being said, I would check it in IAD. If you worry, buy a delayed baggage insurance for $10 that will pay you $500 if your bag is delayed for more than 3 hours. But in general since security tightened airlines behave better with bags on a long layovers.