First off this is an excellent post with a lot of insightful thoughts on hearing that I very much appreciate. However, what someone like Barry Harris has done is in spite of not having much range or good tuning not because of it. Adequate physical technique ALWAYS makes executing what you can hear less effort. Poor technique is often a distraction you have to find a workaround for or simply ignore and settle for its limitations. Unless you're so supremely gifted that great music will emerge from you no matter what you ignore fundamental technique at your peril. Just because there are any number of examples of gifted musicians who have found personal workarounds doesn't mean it's a good general approach to accept.
Just returned to this thread. I didn't mean to imply that proper vocal technique was arbitrary or not worth investing time in, especially when pitch accuracy is concerned. I only meant to emphasize that the singing in this scenario is much more about expanding your aural imagination and that you shouldn't dissuade yourself from vocalizing because you have a limited range at the moment or that it doesn't sound very good etc. I have a lot of students who are very resistant to vocalizing what they're working on because they don't think they have good voices. The sooner they jump that hurdle the sooner they discover how much stronger their aural ideas become.