I figured out why (probably) they didn't try Claire's blood: Angela believes her dreams can't be changed. Saving Nathan using Claire's blood is not what she dreamed, so...

(This is, of course, ignoring questions of whether or not Angela is insane, and also whether or not the "dreams can't be changed" thing has even been consistent throughout the series. Fortunately I no longer care enough about the show to worry much about little things like continuity. Silver lining, hee.)