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In Characteristic numbers for 3-manifolds Milnor and Thurston define a characteristic number and this is cited in ch. 6 of Thurston's notes when discussing the Gromov approach to Mostow rigidity.

The paper opens with "This is a brief report on work which will be published in detail elsewhere", but I can't find the elsewhere (in MR, ZB, the arXiv, or Milnor's collected papers). If this missing paper exists could someone point me to it?

If it doesn't, was something similar written by someone else along the intended line?

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I think that some of their work was preempted by Gromov's (e.g. "Volume and Bounded Cohomology") (which then created a huge research area which I would not want to try to summarize here), but other directions in the paper were continued. See, for example, the beautiful papers by Francaviglia, Frigerio, Martelli and by Sasha Gaifullin

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