Is EAV an appropriate design for a collection of coexisting metadata-rich "fact estimates" on objects?
EAV is not evil; like any other tool, it can be implemented poorly and abused. You can find articles trash talking cursors, dynamic SQL, triggers, even SQL Server itself. That doesn't make them bad things. 

EAV can be an appropriate solution. Whether it's the right answer in your specific case is probably more opinion-based than anything; I'm answering more to suggest that you not close your mind to a solution because someone said it was bad. There are always opposing viewpoints to consider:


What's so bad about EAV, anyway?