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What you are saying is that we are reading the radiation that is going into a black hole along with the radiation that is not going into any black holes. But what about the matter that is already in the black hole? We are not reading any radiation from that matter. We can only be aware of that matter through its gravitational effects.

The problem, as I understand it is, that there seems to be more matter as measured by its gravitational effects than is accounted for by radiation. Since a black hole is exactly the sort of phenomenon that affects its surroundings through gravity but not through radiation, why is it not possible that black holes account for the missing matter?

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I am telling you things every decent physicist knows. It is in any decent book on Cosmology or Astrophysics. The affect of the matter in black holes is completely included in our mass estimates given the radiation we observe from regions of space. The normal matter in black holes is fully accounted for and it is understood theoretically why the matter in black holes affects the radiation spectrum. If you don't believe me, read a book.

Dark matter has nothing to do with black holes. It is basically what you describe, the difference in mass obtained by radiation observation and by observing orbits, however, the mass in black holes is accounted for in the radiation measurements so dark matter is something totally different. If we thought it might be black holes then nobody would care about it. Black holes are understood and have been pretty conclusively observed (google hawking thorne Cygnus to see that they believe that there is conclusive evidence that Cygnus X-1 is a black hole).