"After the usual explanation that it was a “close call”, I asked what I could have done better and was told that I needed to be more consistent."

Probably he just gave another "usual explanation" from his handbook. That's the problem when you have a recruiter as a proxy between you and your interviewer, specially when you get the negative answer. When they get the "No" answer, you are not profitable anymore. You are now a liability. A time-consuming problem they have to deal with. With that couldn't-be-more-generic-feedback, it seems to be your case.

Would be better to reach your interviewers directly and get feedback from them.