Short checking luggage was never a problem for me. And there are myriads of reasons why you want to do this. Take something out to give to somebody, put something in you plan to buy at FRA..... I would expect NO problem and no questions when you ask to short check.
You will still get all of your boarding passes including the FRA-DME.

You always can do an online check in for your other flight before you leave and then just drop the bags.