This seems like a special case of a more general issue that the court must face regularly. Would an argument to the judge like "even if each of these reports comes from a person trying to do a good job in passing along the truth, there are too many places where any of these people could have made a simple error" stand a chance?

No. The lawyer would argue the point to the jury. Unless the judge is the finder of fact because it's a bench trial, the judge doesn't "weigh" the evidence (assess its plausibility). Hearsay is a special case because juries are believed prone to overestimating its reliability and because it implicates the right to confront witnesses.

Long chains of reasoning, on the other hand, aren't likely to mislead the jury. Research on cognitive fluency, in fact, shows people usually discount evidence excessively when it's complicated.