Bad news indeed.
You say that the proffered site behind FRA is totally inappropriate - increased rent and reduced space being one reason. You hinted at other reasons too. It would be helpful to know what these other factors are.
Having another site on the airfield available must surely be the best option to pursue unless the money problem is insurmountable.
I wish the museum the very best of luck and hope this situation can be resolved without splitting the collection or, heaven forbid, losing more airframes.